Dr Lee Zhao

Senior Lecturer

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

Science

School of Mathematics & Statistics

Research Interest: analytic number theory

Employment: Senior Lecturer, Univ. of New South Wales, Jul. 2015 -- Present
Visiting Associate Professor, Brigham Young Univ., Aug. 2013 -- Aug. 2015
Associate Professor, Nanyang Technological Univ., Mar. -- Jul. 2014
Assistant Professor, Nanyang Technological Univ., Jul. 2007 -- Feb. 2013
Postdoctoral Fellow, Royal Inst. of Technology (KTH), Sep. 2006 -- Jul. 2007
Postdoctoral Fellow, Univ. of Toronto, Jul. 2004 -- Jun. 2006
Assistant Professor, United States Military Academy, Jul. 2003 -- Jun. 2004

For more information on me, please go to my personal webpage.

Phone

9385 7086

E-mail

l.zhao@unsw.edu.au

Location

School of Mathematics and Statistics UNSW AUSTRALIA SYDNEY NSW 2052 The Red Centre Room 4106

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, http://dx.doi.org/10.1017/S0004972722001617

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, http://dx.doi.org/10.4064/cm8650-1-2022

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, http://dx.doi.org/10.1142/S1793042123500793

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, http://dx.doi.org/10.1142/s1793042123500793

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, http://dx.doi.org/10.1112/mtk.12219

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, http://dx.doi.org/10.1016/j.jnt.2022.12.007

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, http://dx.doi.org/10.1016/j.jnt.2022.12.007

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, http://dx.doi.org/10.1016/j.ffa.2022.102113

Journal articles | 2023

Gao P; Zhao L, 2023, 'One-level density of quadratic twists of L-functions', Acta Arithmetica, 207, pp. 201 - 215, http://dx.doi.org/10.4064/aa220613-13-12

Journal articles | 2023

Gao P; Zhao L, 2023, 'Ratios conjecture for quadratic Hecke $L$-functions in the Gaussian field', Monatshefte fuer Mathematik, http://arxiv.org/abs/2210.08840v2

Journal articles | 2023

Gao P; Zhao L, 2023, 'Subconvexity of a double Dirichlet series over the Gaussian field', Quarterly Journal of Mathematics, http://dx.doi.org/10.1093/qmath/haad023

Journal articles | 2023

Gao P; Zhao L, 2023, 'Twisted first moment of quadratic and quadratic twist $L$-functions', Functiones et Approximatio Commentarii Mathematici, http://arxiv.org/abs/2301.12615v2

Journal articles | 2023

Gao PENG; Zhao L, 2023, 'LOWER-ORDER TERMS of the ONE-LEVEL DENSITY of A FAMILY of QUADRATIC HECKE -FUNCTIONS', Journal of the Australian Mathematical Society, 114, pp. 178 - 221, http://dx.doi.org/10.1017/S1446788721000410

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, http://dx.doi.org/10.48550/arXiv.1910.09691

Journal articles | 2022

Gao P; Zhao L, 2022, 'Average values of quadratic Hecke character sums', Journal- Ramanujan Mathematical Society, 37, pp. 99 - 107, http://arxiv.org/abs/1910.09691v2

Journal articles | 2022

Gao P; Zhao L, 2022, 'Bounds for moments of cubic and quartic Dirichlet $L$-functions', Indagationes Mathematicae, 33, pp. 1263 - 1296, http://dx.doi.org/10.1016/j.indag.2022.08.003

Journal articles | 2022

Gao P; Zhao L, 2022, 'Bounds for moments of cubic and quartic Dirichlet L-functions', Indagationes Mathematicae, http://dx.doi.org/10.1016/j.indag.2022.08.003

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, http://dx.doi.org/10.7169/facm/1936

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, http://dx.doi.org/10.1017/S1446788720000397

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, http://dx.doi.org/10.1142/S1793042122500877

Journal articles | 2022

2022, 'Moments and One level density of sextic Hecke $L$-functions of $\mathbb{Q}(ω)$', Functiones et Approximatio Commentarii Mathematici, http://arxiv.org/abs/2201.01885v2

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, http://dx.doi.org/10.5802/jtnb.1149

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, http://dx.doi.org/10.5802/jtnb.1149

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, https://www.sciencedirect.com/science/article/pii/S0022314X21001591?via%3Dihub

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, http://arxiv.org/abs/2005.04811v1

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, http://dx.doi.org/10.2140/moscow.2021.10.167

Journal articles | 2020

Gao P; Zhao L, 2020, 'Low-lying zeros of a family of quadratic Hecke $L$-functions via ratios conjecture', , http://arxiv.org/abs/2007.13265v2

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, http://dx.doi.org/10.7169/facm/1857

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, http://dx.doi.org/10.1016/j.jnt.2019.09.002

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, http://dx.doi.org/10.1007/s40993-020-0189-3

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, http://arxiv.org/abs/1708.01701v2

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, http://dx.doi.org/10.1017/S0004972719000224

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, http://arxiv.org/abs/1706.05450v1

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, http://arxiv.org/abs/1912.05041v3

Journal articles | 2019

Gao P; Zhao L, 2019, 'Mean values of some Hecke characters', Acta Arithmetica, 187, pp. 125 - 141, http://dx.doi.org/10.4064/aa170827-9-3

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, http://arxiv.org/abs/1807.09410v1

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, http://arxiv.org/abs/1802.03896v2

Journal articles | 2018

Gao P; Zhao L, 2018, 'Mean values of divisors of forms $n^2+Nm^2$', , http://arxiv.org/abs/1812.07863v1

Journal articles | 2018

Shparlinski IE; Zhao L, 2018, 'Elliptic curves in isogeny classes', Journal of Number Theory, 191, pp. 194 - 212, http://dx.doi.org/10.1016/j.jnt.2018.04.017

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 $\mathbb{Q}(ω)$, http://arxiv.org/abs/1710.04909v2

Journal articles | 2016

Baker RC; Zhao L, 2016, 'Gaps between primes in Beatty sequences', Acta Arithmetica, 172, pp. 207 - 242, http://dx.doi.org/10.4064/aa7993-1-2016

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, http://dx.doi.org/10.1093/imrn/rnw013

Journal articles | 2013

Baier S; Zhao L, 2013, 'On Hecke eigenvalues at primes of the form [g(n)]', Acta Arithmetica, 158, pp. 341 - 357, http://dx.doi.org/10.4064/aa158-4-3

Journal articles | 2013

Foo T; Zhao L, 2013, 'On primes represented by cubic polynomials', Mathematische Zeitschrift, 274, pp. 323 - 340, http://dx.doi.org/10.1007/s00209-012-1072-2

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, http://dx.doi.org/10.1017/S001309151100037X

Journal articles | 2012

Gao P; Zhao L, 2012, 'Large sieve inequalities for quartic characters', Quarterly Journal of Mathematics, 63, pp. 891 - 917, http://dx.doi.org/10.1093/qmath/har018

Journal articles | 2011

Foo T; Zhao L, 2011, 'On Primes Represented by Cubic Polynomials', Math. Z., 2, pp. 1 - 2, http://arxiv.org/abs/1110.1142v2

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, http://dx.doi.org/10.1112/S0010437X10004914

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, http://dx.doi.org/10.1112/jlms/jdp064

Journal articles | 2009

Baier S; Zhao L, 2009, 'On primes in quadratic progressions', International Journal of Number Theory, 5, pp. 1017 - 1035, http://dx.doi.org/10.1142/S1793042109002523

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, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000263773400007&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

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, http://dx.doi.org/10.1090/S0002-9947-08-04498-X

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, http://dx.doi.org/10.1016/j.jnt.2007.03.004

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, http://dx.doi.org/10.1016/j.aim.2008.06.006

Journal articles | 2007

Baier S; Zhao L, 2007, 'Primes in quadratic progressions on average', Mathematische Annalen, 338, pp. 963 - 982, http://dx.doi.org/10.1007/s00208-007-0101-7

Journal articles | 2007

Zhao L, 2007, 'Large sieve inequality with quadratic amplitudes', Monatshefte fur Mathematik, 151, pp. 165 - 173, http://dx.doi.org/10.1007/s00605-006-0408-6

Journal articles | 2006

Baier S; Zhao L, 2006, 'Bombieri-Vinogradov type theorems for sparse sets of moduli', Acta Arithmetica, 125, pp. 187 - 201, http://dx.doi.org/10.4064/aa125-2-5

Journal articles | 2006

Zhao L, 2006, 'Oscillations of Hecke eigenvalues at shifted primes', Revista Matematica Iberoamericana, 22, pp. 323 - 337, http://dx.doi.org/10.4171/RMI/458

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, http://dx.doi.org/10.1142/S1793042105000170

Journal articles | 2005

Baier S; Zhao L, 2005, 'Large Sieve Inequalities for Characters to Powerful Moduli', Int. J. Number Theory, 1, pp. 265 - 279, http://arxiv.org/abs/math/0508130v2

Journal articles | 2005

Zhao L, 2005, 'An improvement of a large sieve inequality in high dimensions', Mathematika, 52, pp. 93 - 100, http://dx.doi.org/10.1112/S0025579300000371

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, http://dx.doi.org/10.4064/aa112-3-5
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, http://dx.doi.org, http://arxiv.org/abs/2201.01885v2
Preprints | 2023

Gao P; Zhao L, 2023, First moment of central values of Hecke $L$-functions with Fixed Order Characters, , http://arxiv.org/abs/2306.10726v1

Preprints | 2023

Gao P; Zhao L, 2023, First moment of central values of quadratic Dirichlet $L$-functions, , http://arxiv.org/abs/2303.11588v1

Preprints | 2023

Gao P; Zhao L, 2023, First moment of central values of some primitive Dirichlet $L$-functions with fixed order characters, , http://arxiv.org/abs/2308.10602v1

Preprints | 2023

Gao P; Zhao L, 2023, Negative first moment of quadratic twists of $L$-functions, , http://arxiv.org/abs/2303.05055v1

Preprints | 2023

Gao P; Zhao L, 2023, Ratios conjecture for quadratic twist of modular $L$-functions, , http://arxiv.org/abs/2304.14600v1

Preprints | 2023

2023, Twisted first moment of quadratic and quadratic twist $L$-functions, , http://arxiv.org/abs/2301.12615v2

Preprints | 2022

Corrigan CC; Zhao L, 2022, Zero-Density Theorems for Families of Dirichlet $L$-functions, , http://arxiv.org/abs/2211.00260v1

Preprints | 2022

Gao P; Zhao L, 2022, Moments of Dirichlet $L$-functions to a fixed modulus over function fields, , http://arxiv.org/abs/2203.14458v2

Preprints | 2022

Gao P; Zhao L, 2022, Moments of quadratic Dirichlet $L$-functions over Function Fields, , http://arxiv.org/abs/2202.07814v3

Preprints | 2022

Gao P; Zhao L, 2022, Non-vanishing of quadratic twists of modular $L$-functions of prime-related moduli, , http://arxiv.org/abs/2205.01824v1

Preprints | 2022

Gao P; Zhao L, 2022, One-level density of quadratic twists of $L$-functions, , http://dx.doi.org/10.4064/aa220613-13-12

Preprints | 2022

2022, Lower bounds for negative moments of $ζ'(ρ)$, , http://arxiv.org/abs/2208.06922v1

Preprints | 2022

2022, Ratios conjecture for quadratic Hecke $L$-functions in the Gaussian field, , http://arxiv.org/abs/2210.08840v2

Preprints | 2022

2022, Subconvexity of a double Dirichlet series over the Gaussian field, , http://arxiv.org/abs/2211.08481v1

Preprints | 2021

Gao P; Zhao L, 2021, Lower bounds for moments of quadratic twists of modular $L$-functions, , http://arxiv.org/abs/2110.02365v2

Preprints | 2016

Shparlinski IE; Zhao L, 2016, Elliptic curves in isogeny classes, , http://dx.doi.org/10.48550/arxiv.1611.05258

Other | 2010

Baier S; Zhao L, 2010, A Subconvexity Bound for Automorphic $L$-functions for $SL(3,Z)$, , http://arxiv.org/abs/1001.2910v4

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, 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, Rutgers University

Analytic number theory

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