Liangyi Zhao

发表

Lower bounds for moments of quadratic twists of modular $L$-functions

Peng Gao, Liangyi Zhao, Peng Gao, 2021, 2110.02365.

LOWER-ORDER TERMS OF THE ONE-LEVEL DENSITY OF A FAMILY OF QUADRATIC HECKE -FUNCTIONS

Peng Gao, Liangyi Zhao, 2019, Journal of the Australian Mathematical Society.

MATC34H3 COMPLEX VARIABLES I, FALL SEMESTER 2005

Liangyi Zhao, Phil Doctor, Saint George Campus, 2005 .

A LOWER BOUND FOR THE LARGE SIEVE WITH SQUARE MODULI

Liangyi Zhao, S. Baier, Sean B. Lynch, 2018, Bulletin of the Australian Mathematical Society.

ON PRIMES IN QUADRATIC PROGRESSIONS

Liangyi Zhao, S. Baier, 2007, math/0701577.

Primes in quadratic progressions on average

Liangyi Zhao, S. Baier, 2006, math/0605563.

Bombieri-Vinogradov Type Theorem for Sparse Sets of Moduli

Liangyi Zhao, S. Baier, 2006, math/0602116.

Lower bounds for negative moments of ζ′(ρ)$\zeta ^{\prime }(\rho )$

Peng Gao, Liangyi Zhao, Peng Gao, 2022, Mathematika.

First moment of central values of quadratic Hecke $L$-functions in the Gaussian field

Peng Gao, Liangyi Zhao, 2022, 2207.03746.

One-level density of quadratic twists of $L$-functions

Peng Gao, Liangyi Zhao, 2022, 2206.02302.

Non-vanishing of quadratic twists of modular $L$-functions of prime-related moduli

Peng Gao, Liangyi Zhao, Peng Gao, 2022, 2205.01824.

Moments and One level density of sextic Hecke $L$-functions of $\mathbb{Q}(\omega)$

Peng Gao, Liangyi Zhao, Peng Gao, 2022, 2201.01885.

Moments of central values of cubic Hecke L-functions of $${\mathbb {Q}}(i)$$

Peng Gao, Liangyi Zhao, Peng Gao, 2018, Research in Number Theory.

Mean values of some Hecke characters

Peng Gao, Liangyi Zhao, Peng Gao, 2017, Acta Arithmetica.

First moment of Hecke L-functions with quartic characters at the central point

Peng Gao, Liangyi Zhao, Peng Gao, 2017, Mathematische Zeitschrift.

Moments and non-vanishing of Hecke $L$-functions with quadratic characters in $\mathbb{Q}(i)$ at the central point

Peng Gao, Liangyi Zhao, Peng Gao, 2017 .

On Hecke eigenvalues at primes of the form $[g(n)]$

Liangyi Zhao, S. Baier, 2011, 1107.1572.

Oscillations of Hecke Eigenvalues at Primes

Liangyi Zhao, 2005, math/0508129.

Large Sieve Inequalities with Quadratic Amplitudes

Liangyi Zhao, 2005, math/0512270.

Moments of quadratic Dirichlet L-functions over function fields

Peng Gao, Liangyi Zhao, 2022, Finite Fields and Their Applications.

Bounds for moments of cubic and quartic Dirichlet L-functions

Liangyi Zhao, Peng Gao, 2022, Indagationes Mathematicae.

Large sieve inequalities for quartic characters

Liangyi Zhao, Peng Gao, 2011, 1101.3646.

Large sieve inequalities for characters to powerful moduli

Liangyi Zhao, S. Baier, 2005, math/0508130.

Negative first moment of quadratic twists of $L$-functions

Liangyi Zhao, Peng Gao, 2023, 2303.05055.

One-level density of quadratic twists of $L$-functions

Liangyi Zhao, Peng Gao, 2022, Acta Arithmetica.

Twisted first moment of quadratic and quadratic twist $L$-functions

Liangyi Zhao, Peng Gao, 2023, 2301.12615.

Low-lying zeros of a family of quadratic Hecke $L$-functions via ratios conjecture

Liangyi Zhao, Peng Gao, 2020, 2007.13265.

One level density of low-lying zeros of quadratic Hecke L-functions to prime moduli

Liangyi Zhao, Peng Gao, 2020, Hardy-Ramanujan Journal.

LOWER-ORDER TERMS OF THE ONE-LEVEL DENSITY OF A FAMILY OF QUADRATIC HECKE $\boldsymbol {L}$ -FUNCTIONS

Liangyi Zhao, Peng Gao, 2019, Journal of the Australian Mathematical Society.

ONE-LEVEL DENSITY OF LOW-LYING ZEROS OF QUADRATIC HECKE L-FUNCTIONS OF IMAGINARY QUADRATIC NUMBER FIELDS

Liangyi Zhao, Peng Gao, 2017, Journal of the Australian Mathematical Society.

One-Level Density of Low-lying Zeros of Quadratic and Quartic Hecke $L$-functions

Liangyi Zhao, Peng Gao, 2017, Canadian Journal of Mathematics.

One level density of low-lying zeros of families of L-functions

Liangyi Zhao, Peng Gao, 2009, Compositio Mathematica.

On Hecke eigenvalues at Piatetski‐Shapiro primes

Liangyi Zhao, S. Baier, 2008, 0808.1756.

On the low-lying zeros of Hasse-Weil L-functions for elliptic curves

Liangyi Zhao, S. Baier, 2007, 0708.2987.

Oscillations of Hecke eigenvalues at shifted primes

Liangyi Zhao, 2006 .

Ratios conjecture for quadratic Hecke L-functions in the Gaussian field

Liangyi Zhao, Peng Gao, 2022, Monatshefte für Mathematik.

Title On primes in quadratic progressions

Liangyi Zhao, 2008 .

First moment of Hecke L-functions with quartic characters at the central point

Peng Gao, Liangyi Zhao, 2019, Mathematische Zeitschrift.

Averages of shifted convolutions of d3(n)

Liangyi Zhao, S. Baier, T. Browning, 2011, Proceedings of the Edinburgh Mathematical Society.

First moment of central values of Hecke $L$-functions with Fixed Order Characters

Liangyi Zhao, Peng Gao, 2023, 2306.10726.

Moments and One level density of certain unitary families of Hecke L-functions

Liangyi Zhao, Peng Gao, 2018, 1808.01710.

Weighted first moments of some special quadratic Dirichlet L-functions

Liangyi Zhao, Peng Gao, 2018, New Zealand Journal of Mathematics.

Value-distribution of quartic Hecke L-functions

Peng Gao, Liangyi Zhao, Liangyi Zhao, 2018, Moscow Journal of Combinatorics and Number Theory.

Ratios conjecture for primitive quadratic Hecke $L$-functions

Liangyi Zhao, Peng Gao, 2023, 2309.13811.

First moment of central values of some primitive Dirichlet $L$-functions with fixed order characters

Liangyi Zhao, Peng Gao, 2023, 2308.10602.

Ratios conjecture for quadratic twist of modular $L$-functions

Liangyi Zhao, Peng Gao, 2023, 2304.14600.

First moment of central values of quadratic Dirichlet $L$-functions

Liangyi Zhao, Peng Gao, 2023, 2303.11588.

Mean squares of quadratic twists of the Möbius function

Liangyi Zhao, Peng Gao, 2022, Journal of Number Theory.

Subconvexity of a double Dirichlet series over the Gaussian field

Liangyi Zhao, Peng Gao, 2022, The Quarterly Journal of Mathematics.

First moment of central values of quadratic Hecke L-functions in the Gaussian field

Liangyi Zhao, Peng Gao, 2022, International Journal of Number Theory.

Moments of Dirichlet $L$-functions to a fixed modulus over function fields

Liangyi Zhao, Peng Gao, 2022, 2203.14458.

Lower bounds for moments of quadratic twists of modular $L$-functions

Liangyi Zhao, Peng Gao, 2021, 2110.02365.

Bounds for moments of quadratic Dirichlet $L$-functions of prime-related moduli

Liangyi Zhao, Peng Gao, 2021, Colloquium Mathematicum.

Bounds for moments of cubic and quartic Dirichlet L-functions

Liangyi Zhao, Peng Gao, 2021, Indagationes Mathematicae.

Moments of central values of quartic Dirichlet $L$-functions

Peng Gao, Liangyi Zhao, Liangyi Zhao, 2021, 2102.02373.

The large sieve with power moduli in imaginary quadratic number fields

Peng Gao, Liangyi Zhao, Liangyi Zhao, 2021, International Journal of Number Theory.

First moments of some Hecke $L$-functions of prime moduli

Liangyi Zhao, Peng Gao, 2020, Functiones et Approximatio Commentarii Mathematici.

Moments of central values of cubic Hecke L-functions of Q(i)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {

Liangyi Zhao, Peng Gao, 2020, Research in Number Theory.

Average values of quadratic Hecke character sums

Liangyi Zhao, Peng Gao, 2019, 1910.09691.

Mean values of cubic and quartic Dirichlet characters

Liangyi Zhao, Peng Gao, 2019, 1902.10987.

Mean values of divisors of forms $n^2+Nm^2$

Liangyi Zhao, Peng Gao, 2018, 1812.07863.

Primes $p \equiv 1 \bmod{d}$ and $a^{(p-1)/d} \equiv 1 \bmod{p}$}.

Liangyi Zhao, Peng Gao, 2018 .

Primes $p \equiv 1 \bmod{d}$ and $a^{(p-1)/d} \equiv 1 \bmod{p}$}

Liangyi Zhao, Peng Gao, 2018, 1807.09410.

Moments and One level density of quadratic Hecke $L$-functions of $\mathbb{Q}(\omega)$

Liangyi Zhao, Peng Gao, 2017, 1710.04909.

Moments of quadratic Hecke L-functions of imaginary quadratic number fields

Liangyi Zhao, Peng Gao, 2017, Journal of Number Theory.

Elliptic curves in isogeny classes

I. Shparlinski, Liangyi Zhao, 2016, Journal of Number Theory.

On primes represented by cubic polynomials

Liangyi Zhao, Timothy Foo, 2012, Mathematische Zeitschrift.

On primes represented by cubic polynomials

Liangyi Zhao, Timothy Foo, 2011, 1110.1142.

A Subconvexity Bound for Automorphic $L$-functions for $SL(3,Z)$

Liangyi Zhao, S. Baier, 2010, 1001.2910.

The Sato-Tate conjecture on average for small angles

Liangyi Zhao, S. Baier, 2006, math/0608318.

BURGESS BOUND FOR CHARACTER SUMS

Liangyi Zhao, 2007 .

Title Primes in quadratic progressions on average

Liangyi Zhao, 2007 .

Large Sieve Inequality with Quadratic Amplitudes

Liangyi Zhao, 2007 .

AN IMPROVEMENT FOR THE LARGE SIEVE FOR SQUARE MODULI

Liangyi Zhao, S. Baier, 2005, math/0512271.

Study on Deep Learning Technology to Construct E-Commerce Industry Marketing Promotion Model

Liangyi Zhao, Peng Gao, 2022, Security and Communication Networks.

A large sieve inequality for quartic characters

Liangyi Zhao, Peng Gao, 2011 .

On primes represented by quadratic polynomials

Liangyi Zhao, Stephan Baier, Liangyi Zhao, 2007, math/0703284.

Gaps of Smallest Possible Order between Primes in an Arithmetic Progression

R. Baker, Liangyi Zhao, 2014, 1412.0574.