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Dr Lee Zhao

Dr Lee Zhao

Senior Lecturer

Ph. D., Rutgers University, May 2003
B. A., Rutgers University, May 1998

Science
School of Mathematics & Statistics

My primary research interests are in analytic number theory.  More specifically, I am interested in the analytic theory of of L-functions, exponential sums, the large sieve, elliptic curves.  I joined the School of Mathematics and Statistics at in 2015.  For more information, please go to my .
Phone
02 9385 7086
E-mail
l.zhao@unsw.edu.au
Location
School of Mathematics and Statistics AUSTRALIA SYDNEY NSW 2052 The Red Centre Room 4106
  • Journal articles | 2024
    Gao P; Zhao L, 2024, 'Bounds for moments of quadratic Dirichlet character sums', Bulletin of the Australian Mathematical Society
    Journal articles | 2024
    Gao P; Zhao L, 2024, 'First moment of central values of some primitive Dirichlet $L$-functions with fixed order characters', Journal of Number Theory, 261, pp. 125 - 142
    Journal articles | 2024
    Gao P; Zhao L, 2024, 'First moment of central values of some primitive Dirichlet L-functions with fixed order characters', Journal of Number Theory, 261, pp. 125 - 142,
    Journal articles | 2024
    Gao P; Zhao L, 2024, 'Lower Bounds for Moments of Quadratic Twists of Modular L-functions', Functiones et Approximatio Commentarii Mathematici
    Journal articles | 2024
    Gao P; Zhao L, 2024, 'Moments and one level density of sextic Hecke L-functions', Functiones et Approximatio Commentarii Mathematici, 70, pp. 7 - 28,
    Journal articles | 2024
    Gao P; Zhao L, 2024, 'Moments of Dirichlet $L$-functions to a fixed modulus over function fields', International Journal of Number Theory
    Journal articles | 2024
    Gao P; Zhao L, 2024, 'Moments of Dirichlet L-functions to a fixed modulus over function fields', International Journal of Number Theory, 20, pp. 1493 - 1513,
    Journal articles | 2024
    Gao P; Zhao L, 2024, 'Ratios conjecture for quadratic twists of modular $L$-functions', Research in Number Theory, 10,
    Journal articles | 2024
    Gao P; Zhao L, 2024, 'Twisted first moment of quadratic and quadratic twist $L$-functions', Functiones et Approximatio Commentarii Mathematici, 70, pp. 101 - 127,
    Journal articles | 2023
    Corrigan C; Zhao L, 2023, 'Zero-Density Theorems for Families of Dirichlet L-functions', Bulletin of the Australian Mathematical Society, 108, pp. 224 - 235,
    Journal articles | 2023
    Gao P; Zhao L, 2023, 'Bounds for moments of quadratic Dirichlet $L$-functions of prime-related moduli', Colloquium Mathematicum, 171, pp. 61 - 77,
    Journal articles | 2023
    Gao P; Zhao L, 2023, 'First moment of central values of quadratic Hecke $L$-functions in the Gaussian field', International Journal of Number Theory,
    Journal articles | 2023
    Gao P; Zhao L, 2023, 'First moment of central values of quadratic Hecke L-functions in the Gaussian field', International Journal of Number Theory, 19, pp. 1621 - 1637,
    Journal articles | 2023
    Gao P; Zhao L, 2023, 'Lower bounds for negative moments of $ζ'(ρ)$', Mathematika: a journal of pure and applied mathematics, 69, pp. 1081 - 1103,
    Journal articles | 2023
    Gao P; Zhao L, 2023, 'Mean squares of quadratic twists of the Möbius function', Journal of Number Theory, 247, pp. 1 - 14,
    Journal articles | 2023
    Gao P; Zhao L, 2023, 'Mean squares of quadratic twists of the Möbius function', Journal of Number Theory, 247, pp. 1 - 14,
    Journal articles | 2023
    Gao P; Zhao L, 2023, 'Moments of quadratic Dirichlet L-functions over function fields', Finite Fields and Their Applications, 85, pp. 102113 - 102113,
    Journal articles | 2023
    Gao P; Zhao L, 2023, 'One-level density of quadratic twists of L-functions', Acta Arithmetica, 207, pp. 201 - 215,
    Journal articles | 2023
    Gao P; Zhao L, 2023, 'Ratios conjecture for quadratic Hecke $L$-functions in the Gaussian field', Monatshefte fuer Mathematik,
    Journal articles | 2023
    Gao P; Zhao L, 2023, 'Ratios conjecture for quadratic Hecke L-functions in the Gaussian field', Monatshefte fur Mathematik, 203, pp. 63 - 90,
    Journal articles | 2023
    Gao P; Zhao L, 2023, 'Subconvexity of a double Dirichlet series over the Gaussian field', Quarterly Journal of Mathematics, 74, pp. 1237 - 1252,
    Journal articles | 2023
    Gao PENG; Zhao L, 2023, 'Lower-order terms of the one-level density of a family of quadratic Hecke L-functions', Journal of the Australian Mathematical Society, 114, pp. 178 - 221,
    Journal articles | 2022
    Gao P; Zhao L, 2022, 'Average values of quadratic Hecke character sums', Journal of the Ramanujan Mathematical Society, 37, pp. 99 - 107,
    Journal articles | 2022
    Gao P; Zhao L, 2022, 'Bounds for moments of cubic and quartic Dirichlet $L$-functions', Indagationes Mathematicae, 33, pp. 1263 - 1296,
    Journal articles | 2022
    Gao P; Zhao L, 2022, 'Bounds for moments of cubic and quartic Dirichlet L-functions', Indagationes Mathematicae,
    Journal articles | 2022
    Gao P; Zhao L, 2022, 'First Moments of Some Hecke $L$-functions of Prime Moduli', Functiones et Approximatio Commentarii Mathematici, 66, pp. 161 - 178,
    Journal articles | 2022
    Gao P; Zhao L, 2022, 'One level density of low-lying zeros of quadratic Hecke $L$-functions of Imaginary Quadratic Number Fields', Journal of the Australian Mathematical Society, 112, pp. 170 - 192,
    Journal articles | 2022
    Gao P; Zhao L, 2022, 'The Large Sieve with Power Moduli in Imaginary Quadratic Number Fields', International Journal of Number Theory, 18, pp. 1713 - 1733,
    Journal articles | 2022
    Gao P; Zhao L, 2022, 'Moments of quadratic Dirichlet $L$-functions over Function Fields', Finite Fields and Their Applications
    Journal articles | 2021
    Gao P; Zhao L, 2021, 'Moments and One level density of certain unitary families of Hecke {$L$}-functions', Journal de Theorie des Nombres de Bordeaux, 33, pp. 1 - 16,
    Journal articles | 2021
    Gao P; Zhao L, 2021, 'Moments and One level density of certain unitary families of Hecke L-functions', JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX, 33, pp. 1 - 16,
    Journal articles | 2021
    Gao P; Zhao L, 2021, 'Moments of central values of quartic Dirichlet L-functions', Journal of Number Theory, 228, pp. 342 - 358,
    Journal articles | 2021
    Gao P; Zhao L, 2021, 'One level density of low-lying zeros of quadratic Hecke $L$-functions to prime moduli', The Hardy-Ramanujan Journal, 43, pp. 173 - 187
    Journal articles | 2021
    Gao P; Zhao L, 2021, 'Value-distribution of quartic Hecke $L$-functions', Moscow Journal of Combinatorics and Number Theory, 10, pp. 167 - 181,
    Journal articles | 2020
    Gao P; Zhao L, 2020, 'First Moments of Some Hecke $L$-functions of Prime Moduli', Funct. Approx. Comment. Math., Vol. 66, 2022, No. 2, pp. 161--178,
    Journal articles | 2020
    Gao P; Zhao L, 2020, 'Low-lying zeros of a family of quadratic Hecke $L$-functions via ratios conjecture', ,
    Journal articles | 2020
    Gao P; Zhao L, 2020, 'Mean values of cubic and quartic Dirichlet Characters', Functiones et Approximatio Commentarii Mathematici, 63, pp. 227 - 245,
    Journal articles | 2020
    Gao P; Zhao L, 2020, 'Moments of Quadratic Hecke $L$-functions of Imaginary Quadratic Number Fields', Journal of Number Theory, 209, pp. 359 - 377,
    Journal articles | 2020
    Gao P; Zhao L, 2020, 'Moments of central values of cubic Hecke $L$-functions of $\mathbb{Q}(i)$', Research in Number Theory, 6, pp. 14,
    Journal articles | 2020
    Gao P; Zhao L, 2020, 'One level density of low-lying zeros of quadratic Hecke L-functions to prime moduli', Hardy-Ramanujan Journal, 43, pp. 173 - 187,
    Journal articles | 2020
    Gao P; Zhao L, 2020, 'One level density of low-lying zeros of quadratic and quartic Hecke $L$-functions', Canadian Journal of Mathematics, 72, pp. 427 - 454,
    Journal articles | 2019
    Baier S; Lynch S; Zhao L, 2019, 'A Lower Bound for the Large Sieve with Square Moduli', Bulletin of the Australian Mathematical Society, 100, pp. 225 - 225,
    Journal articles | 2019
    Gao P; Zhao L, 2019, 'Average values of quadratic Hecke character sums', Journal- Ramanujan Mathematical Society, 37, pp. 99 - 107
    Journal articles | 2019
    Gao P; Zhao L, 2019, 'First Moment of Hecke $L$-functions with quartic characters at the central point', Mathematische Zeitschrift, 294, pp. 1841 - 1854,
    Journal articles | 2019
    Gao P; Zhao L, 2019, 'Lower order terms of the one level density of a family of quadratic Hecke $L$-functions', Journal of the Australian Mathematical Society
    Journal articles | 2019
    Gao P; Zhao L, 2019, 'Mean values of some Hecke characters', Acta Arithmetica, 187, pp. 125 - 141,
    Journal articles | 2019
    Gao P; Zhao L, 2019, 'PRIMES p ≡ 1 mod d AND a(p1)/d ≡ 1 mod p', Integers, 19
    Journal articles | 2019
    Gao P; Zhao L, 2019, 'Primes $p \equiv 1 \bmod{d}$ and $a^{(p-1)/d} \equiv 1 \bmod{p}$}', Integers : Electronic Journal of Combinatorial Number Theory, 19
    Journal articles | 2019
    Gao P; Zhao L, 2019, 'WEIGHTED FIRST MOMENTS OF SOME SPECIAL QUADRATIC DIRICHLET L-FUNCTIONS', New Zealand Journal of Mathematics, 49, pp. 31 - 40
    Journal articles | 2019
    Gao P; Zhao L, 2019, 'Weighted first moments of some special quadratic Dirichlet $L$-functions', New Zealand Journal of Mathematics, 49, pp. 31 - 40
    Journal articles | 2018
    Gao P; Zhao L, 2018, 'Mean values of divisors of forms $n^2+Nm^2$', ,
    Journal articles | 2018
    Shparlinski IE; Zhao L, 2018, 'Elliptic curves in isogeny classes', Journal of Number Theory, 191, pp. 194 - 212
    Journal articles | 2017
    Gao P; Zhao L, 2017, 'Moments and One level density of quadratic Hecke $L$-functions of $\mathbb{Q}(ω)$', Moments and One level density of quadratic Hecke $L$-functions of $\mathbb{Q}(ω)$,
    Journal articles | 2016
    Baker RC; Zhao L, 2016, 'Gaps between primes in Beatty sequences', Acta Arithmetica, 172, pp. 207 - 242,
    Journal articles | 2016
    Baker RC; Zhao L, 2016, 'Gaps of Smallest Possible Order between Primes in an Arithmetic Progression', International Mathematics Research Notices, 2016, pp. 7341 - 7368,
    Journal articles | 2013
    Baier S; Zhao L, 2013, 'On Hecke eigenvalues at primes of the form [g(n)]', Acta Arithmetica, 158, pp. 341 - 357,
    Journal articles | 2013
    Foo T; Zhao L, 2013, 'On primes represented by cubic polynomials', Mathematische Zeitschrift, 274, pp. 323 - 340,
    Journal articles | 2012
    Baier S; Browning TD; Marasingha G; Zhao L, 2012, 'Averages of shifted convolutions of d3(n)', Proceedings of the Edinburgh Mathematical Society, 55, pp. 551 - 576,
    Journal articles | 2012
    Gao P; Zhao L, 2012, 'Large sieve inequalities for quartic characters', Quarterly Journal of Mathematics, 63, pp. 891 - 917,
    Journal articles | 2011
    Foo T; Zhao L, 2011, 'On Primes Represented by Cubic Polynomials', Math. Z., 2, pp. 1 - 2
    Journal articles | 2011
    Gao P; Zhao L, 2011, 'One level density of low-lying zeros of families of L-functions', Compositio Mathematica, 147, pp. 1 - 18,
    Journal articles | 2010
    Baier S; Zhao L, 2010, 'On Hecke eigenvalues at Piatetski-Shapiro primes', Journal of the London Mathematical Society, 81, pp. 175 - 201,
    Journal articles | 2009
    Baier S; Zhao L, 2009, 'On primes in quadratic progressions', International Journal of Number Theory, 5, pp. 1017 - 1035,
    Journal articles | 2009
    Baier S; Zhao L, 2009, 'THE SATO-TATE CONJECTURE ON AVERAGE FOR SMALL ANGLES', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 361, pp. 1811 - 1832
    Journal articles | 2009
    Baier S; Zhao L, 2009, 'The sato-tate conjecture on average for small angles', Transactions of the American Mathematical Society, 361, pp. 1811 - 1832,
    Journal articles | 2008
    Baier S; Zhao L, 2008, 'An improvement for the large sieve for square moduli', Journal of Number Theory, 128, pp. 154 - 174,
    Journal articles | 2008
    Baier S; Zhao L, 2008, 'On the low-lying zeros of Hasse-Weil L-functions for elliptic curves', Advances in Mathematics, 219, pp. 952 - 985,
    Journal articles | 2007
    Baier S; Zhao L, 2007, 'Primes in quadratic progressions on average', Mathematische Annalen, 338, pp. 963 - 982,
    Journal articles | 2007
    Zhao L, 2007, 'Large sieve inequality with quadratic amplitudes', Monatshefte fur Mathematik, 151, pp. 165 - 173,
    Journal articles | 2006
    Baier S; Zhao L, 2006, 'Bombieri-Vinogradov type theorems for sparse sets of moduli', Acta Arithmetica, 125, pp. 187 - 201,
    Journal articles | 2006
    Zhao L, 2006, 'Oscillations of Hecke eigenvalues at shifted primes', Revista Matematica Iberoamericana, 22, pp. 323 - 337,
    Journal articles | 2005
    Baier S; Zhao L, 2005, 'LARGE SIEVE INEQUALITY WITH CHARACTERS FOR POWERFUL MODULI', INTERNATIONAL JOURNAL OF NUMBER THEORY, 1, pp. 265 - 279,
    Journal articles | 2005
    Baier S; Zhao L, 2005, 'Large Sieve Inequalities for Characters to Powerful Moduli', Int. J. Number Theory, 1, pp. 265 - 279
    Journal articles | 2005
    Zhao L, 2005, 'An improvement of a large sieve inequality in high dimensions', Mathematika, 52, pp. 93 - 100,
    Journal articles | 2004
    Zhao L, 2004, 'Large Sieve Inequalities for Special Characters to Prime Square Moduli', Functiones et Approximatio, Commentarii Mathematici, 32, pp. 99 - 106
    Journal articles | 2004
    Zhao L, 2004, 'Large sieve inequality with characters to square moduli', Acta Arithmetica, 112, pp. 297 - 308,
  • Working Papers | 2022
    Gao P; Zhao L, 2022, Moments and One level density of sextic Hecke $L$-functions of $\mathbb{Q}(ω)$, Adam Mickiewicz University Press, ,
    Working Papers | 2022
    Gao P; Zhao L, 2022, Moments and one level density of sextic Hecke L-functions of Q(ω), ,
    Working Papers | 2022
    Gao P; Zhao L, 2022, Ratios conjecture for quadratic Hecke L-functions in the Gaussian field, ,
  • Preprints | 2024
    Gao P; Zhao L, 2024, Bounds for moments of quadratic Dirichlet character sums, ,
    Preprints | 2024
    Gao P; Zhao L, 2024, Ratios conjecture of quadratic Hecke $L$-functions of prime-related moduli, ,
    Preprints | 2024
    Gao P; Zhao L, 2024, Ratios conjecture of quartic $L$-functions of prime moduli, ,
    Preprints | 2024
    Gao P; Zhao L, 2024, Twisted first moment of central values of primitive quadratic Dirichlet $L$-functions, ,
    Preprints | 2023
    Gao P; Zhao L, 2023, First moment of central values of Hecke $L$-functions with Fixed Order Characters, ,
    Preprints | 2023
    Gao P; Zhao L, 2023, First moment of central values of quadratic Dirichlet $L$-functions,
    Preprints | 2023
    Gao P; Zhao L, 2023, First moment of central values of some primitive Dirichlet $L$-functions with fixed order characters, ,
    Preprints | 2023
    Gao P; Zhao L, 2023, First moment of central values of some primitive Dirichlet $L$-functions with fixed order characters, ,
    Preprints | 2023
    Gao P; Zhao L, 2023, Negative first moment of quadratic twists of $L$-functions,
    Preprints | 2023
    Gao P; Zhao L, 2023, Ratios conjecture for primitive quadratic Hecke $L$-functions, ,
    Preprints | 2023
    Gao P; Zhao L, 2023, Ratios conjecture for quadratic twist of modular $L$-functions, ,
    Preprints | 2023
    Gao P; Zhao L, 2023, Ratios conjecture of cubic $L$-functions of prime moduli, ,
    Preprints | 2023
    Gao P; Zhao L, 2023, Twisted first moment of quadratic and quadratic twist $L$-functions, ,
    Preprints | 2023
    2023, Twisted first moment of quadratic and quadratic twist $L$-functions, ,
    Preprints | 2022
    Corrigan CC; Zhao L, 2022, Zero-Density Theorems for Families of Dirichlet $L$-functions, ,
    Preprints | 2022
    Gao P; Zhao L, 2022, First moment of central values of quadratic Hecke $L$-functions in the Gaussian field, ,
    Preprints | 2022
    Gao P; Zhao L, 2022, Lower bounds for negative moments of $\zeta'(\rho)$, ,
    Preprints | 2022
    Gao P; Zhao L, 2022, Mean squares of quadratic twists of the Möbius function, ,
    Preprints | 2022
    Gao P; Zhao L, 2022, Moments and One level density of sextic Hecke $L$-functions of $\mathbb{Q}(\omega)$, ,
    Preprints | 2022
    Gao P; Zhao L, 2022, Moments of Dirichlet $L$-functions to a fixed modulus over function fields, ,
    Preprints | 2022
    Gao P; Zhao L, 2022, Moments of quadratic Dirichlet $L$-functions over Function Fields,
    Preprints | 2022
    Gao P; Zhao L, 2022, Non-vanishing of quadratic twists of modular $L$-functions of prime-related moduli, ,
    Preprints | 2022
    Gao P; Zhao L, 2022, One-level density of quadratic twists of $L$-functions, ,
    Preprints | 2022
    Gao P; Zhao L, 2022, Ratios conjecture for quadratic Hecke $L$-functions in the Gaussian field, ,
    Preprints | 2022
    Gao P; Zhao L, 2022, Subconvexity of a double Dirichlet series over the Gaussian field, ,
    Preprints | 2022
    2022, Lower bounds for negative moments of $ζ'(ρ)$, ,
    Preprints | 2022
    2022, Ratios conjecture for quadratic Hecke $L$-functions in the Gaussian field, ,
    Preprints | 2022
    2022, Subconvexity of a double Dirichlet series over the Gaussian field, ,
    Preprints | 2021
    Gao P; Zhao L, 2021, Bounds for moments of cubic and quartic Dirichlet $L$-functions, ,
    Preprints | 2021
    Gao P; Zhao L, 2021, Bounds for moments of quadratic Dirichlet $L$-functions of prime-related moduli, ,
    Preprints | 2021
    Gao P; Zhao L, 2021, Lower bounds for moments of quadratic twists of modular $L$-functions, ,
    Preprints | 2021
    Gao P; Zhao L, 2021, Moments of central values of quartic Dirichlet $L$-functions, ,
    Preprints | 2019
    Gao P; Zhao L, 2019, Lower order terms of the one level density of a family of quadratic Hecke $L$-functions, ,
    Preprints | 2019
    Gao P; Zhao L, 2019, Mean values of cubic and quartic Dirichlet Characters, ,
    Preprints | 2018
    Baier S; Lynch SB; Zhao L, 2018, A Lower Bound for the Large Sieve with Square Moduli, ,
    Preprints | 2018
    Gao P; Zhao L, 2018, Moments and One level density of certain unitary families of Hecke {$L$}-functions, ,
    Preprints | 2018
    Gao P; Zhao L, 2018, Value-distribution of quartic Hecke $L$-functions, ,
    Preprints | 2017
    Gao P; Zhao L, 2017, First Moment of Hecke $L$-functions with quartic characters at the central point, ,
    Preprints | 2017
    Gao P; Zhao L, 2017, Moments of Quadratic Hecke $L$-functions of Imaginary Quadratic Number Fields, ,
    Preprints | 2017
    Gao P; Zhao L, 2017, One level density of low-lying zeros of quadratic Hecke $L$-functions of Imaginary Quadratic Number Fields, ,
    Preprints | 2016
    Shparlinski IE; Zhao L, 2016, Elliptic curves in isogeny classes, ,
    Other | 2010
    Baier S; Zhao L, 2010, A Subconvexity Bound for Automorphic $L$-functions for $SL(3,Z)$, ,
    Preprints | 2009
    Gao P; Zhao L, 2009, One level density of low-lying zeros of families of $L$-functions, ,
    Preprints | 2008
    Baier S; Zhao L, 2008, On Hecke Eigenvalues at Piatetski-Shapiro Primes, ,
    Preprints | 2007
    Baier S; Zhao L, 2007, On the Low-lying zeros of Hasse-Weil L-functions for Elliptic Curves, ,
    Preprints | 2006
    Baier S; Zhao L, 2006, Bombieri-Vinogradov Type Theorem for Sparse Sets of Moduli, ,
    Conference Papers | 2006
    Zhao L; Baier S, 2006, 'On Primes Represented by Quadratic Polynomials', in de Koninck J; Granville A; Luca F (eds.), Anatomy of Integers, Montreal, pp. 159 - 166, presented at Anatomy of Integers, Montreal, 13 November 2006 - 17 March 2006
    Theses / Dissertations | 2003
    Zhao L, 2003, Large Sieve and Exponential Sums

Faculty Research Grant, Sydney Australia, 2017, 2018, 2019, 2020, 2021, 2023, 2024

Faculty Goldstar Grant, Sydney Australia, 2019

Faculty Silverstar Grant, Sydney Australia, 2022, 2018

Academic Research Fund Tier 1 Grant, Nanyang Tech. Univ., Singapore, Feb. 2010 – Feb. 2013

Max-Planck-Institut f¨ur Mathematik Research Grant, Bonn Germany Jan. – Jun. 2010

Academic Research Fund Tier 1 Grant, Nanyang Tech. Univ., Singapore, Jan. 2008 – Jan. 2010

Commander’s Award for Civilian Service, U. S. Mil. Acad., 2004

Davies Fellowship, US Mil. Acad. & US Army Research Lab. 2004

Analytic number theory

President, Number Theory Down Under, Sep. 2023 -- Present

My Teaching

I teach a variety of undergraduate and graduate courses in pure mathematics.