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Moments and equidistributions of multiplicative analogues of Kloosterman sums SCIE
期刊论文 | 2022 , 206 (3) , 245-275 | ACTA ARITHMETICA
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Keyword :

arcsine law character sum Dirichlet L-function equidistribution Kloosterman sum moment

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GB/T 7714 Xi, Ping . Moments and equidistributions of multiplicative analogues of Kloosterman sums [J]. | ACTA ARITHMETICA , 2022 , 206 (3) : 245-275 .
MLA Xi, Ping . "Moments and equidistributions of multiplicative analogues of Kloosterman sums" . | ACTA ARITHMETICA 206 . 3 (2022) : 245-275 .
APA Xi, Ping . Moments and equidistributions of multiplicative analogues of Kloosterman sums . | ACTA ARITHMETICA , 2022 , 206 (3) , 245-275 .
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Sign Changes of Kloosterman Sums with Almost Prime Moduli. II: Corrigendum SCIE Scopus
期刊论文 | 2022 , 2022 (1) , 556-574 | INTERNATIONAL MATHEMATICS RESEARCH NOTICES
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Abstract :

We give a corrigendum to the previous paper [8] and recover the same quantitative statement: the Kloosterman sum changes sign infinitely often as the modulus runs over squarefree numbers with at most seven prime factors.

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GB/T 7714 Xi, Ping . Sign Changes of Kloosterman Sums with Almost Prime Moduli. II: Corrigendum [J]. | INTERNATIONAL MATHEMATICS RESEARCH NOTICES , 2022 , 2022 (1) : 556-574 .
MLA Xi, Ping . "Sign Changes of Kloosterman Sums with Almost Prime Moduli. II: Corrigendum" . | INTERNATIONAL MATHEMATICS RESEARCH NOTICES 2022 . 1 (2022) : 556-574 .
APA Xi, Ping . Sign Changes of Kloosterman Sums with Almost Prime Moduli. II: Corrigendum . | INTERNATIONAL MATHEMATICS RESEARCH NOTICES , 2022 , 2022 (1) , 556-574 .
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Kloosterman Sums and a Problem of D. H. Lehmer SCIE CSCD
期刊论文 | 2020 , 41 (3) , 361-370 | CHINESE ANNALS OF MATHEMATICS SERIES B | IF: 0.756
WoS CC Cited Count: 2
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Abstract :

A classical problem of D. H. Lehmer suggests the study of distributions of elements of Z/pZ of opposite parity to the multiplicative inverse mod p. Zhang initiated this problem and found an asymptotic evaluation of the number of such elements. In this paper, an asymptotic formula for the fourth moment of the error term of Zhang is proved, from which one may see that Zhang's error term is optimal up to the logarithm factor. The method also applies to the case of arbitrary positive integral moments.

Keyword :

D H Kloosterman sum Lehmer problem Moment

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GB/T 7714 Xi, Ping , Yi, Yuan . Kloosterman Sums and a Problem of D. H. Lehmer [J]. | CHINESE ANNALS OF MATHEMATICS SERIES B , 2020 , 41 (3) : 361-370 .
MLA Xi, Ping 等. "Kloosterman Sums and a Problem of D. H. Lehmer" . | CHINESE ANNALS OF MATHEMATICS SERIES B 41 . 3 (2020) : 361-370 .
APA Xi, Ping , Yi, Yuan . Kloosterman Sums and a Problem of D. H. Lehmer . | CHINESE ANNALS OF MATHEMATICS SERIES B , 2020 , 41 (3) , 361-370 .
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When Kloosterman sums meet Hecke eigenvalues SCIE Scopus
期刊论文 | 2020 , 220 (1) , 61-127 | INVENTIONES MATHEMATICAE
WoS CC Cited Count: 1 SCOPUS Cited Count: 2
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By elaborating a two-dimensional Selberg sieve with asymptotics and equidistributions of Kloosterman sums from l\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell $$\end{document}-adic cohomology, as well as a Bombieri-Vinogradov type mean value theorem for Kloosterman sums in arithmetic progressions, it is proved that for any given primitive Hecke-Maass cusp form of trivial nebentypus, the eigenvalue of the n-th Hecke operator does not coincide with the Kloosterman sum Kl(1,n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {Kl}(1,n)$$\end{document} for infinitely many squarefree n with at most 100 prime factors. This provides a partial negative answer to a problem of Katz on modular structures of Kloosterman sums.

Keyword :

11F30 11L05 11N36 11T23

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GB/T 7714 Xi, Ping . When Kloosterman sums meet Hecke eigenvalues [J]. | INVENTIONES MATHEMATICAE , 2020 , 220 (1) : 61-127 .
MLA Xi, Ping . "When Kloosterman sums meet Hecke eigenvalues" . | INVENTIONES MATHEMATICAE 220 . 1 (2020) : 61-127 .
APA Xi, Ping . When Kloosterman sums meet Hecke eigenvalues . | INVENTIONES MATHEMATICAE , 2020 , 220 (1) , 61-127 .
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Sign Changes of Kloosterman Sums with Almost Prime Moduli. II SCIE
期刊论文 | 2018 , 2018 (4) , 1200-1227 | INTERNATIONAL MATHEMATICS RESEARCH NOTICES | IF: 1.452
WoS CC Cited Count: 3
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We prove that the Kloosterman sum S(1, 1; c) changes sign infinitely often as c runs over squarefree numbers with at most 7 prime factors, which improves the previous results of Fouvry and Michel, Sivak-Fischler, Matomaki, and the author.

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GB/T 7714 Xi, Ping . Sign Changes of Kloosterman Sums with Almost Prime Moduli. II [J]. | INTERNATIONAL MATHEMATICS RESEARCH NOTICES , 2018 , 2018 (4) : 1200-1227 .
MLA Xi, Ping . "Sign Changes of Kloosterman Sums with Almost Prime Moduli. II" . | INTERNATIONAL MATHEMATICS RESEARCH NOTICES 2018 . 4 (2018) : 1200-1227 .
APA Xi, Ping . Sign Changes of Kloosterman Sums with Almost Prime Moduli. II . | INTERNATIONAL MATHEMATICS RESEARCH NOTICES , 2018 , 2018 (4) , 1200-1227 .
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TERNARY DIVISOR FUNCTIONS IN ARITHMETIC PROGRESSIONS TO SMOOTH MODULI SCIE Scopus
期刊论文 | 2018 , 64 (3) , 701-729 | MATHEMATIKA | IF: 0.689
SCOPUS Cited Count: 1
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Abstract :

We prove that the exponent of distribution of tau 3 in arithmetic progressions can be as large as 1/2 + 1/34, provided that the moduli is squarefree and has only sufficiently small prime factors. The tools involve arithmetic exponent pairs for algebraic trace functions, as well as a double q-analogue of the van der Corput method for smooth bilinear forms.

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GB/T 7714 Xi, Ping . TERNARY DIVISOR FUNCTIONS IN ARITHMETIC PROGRESSIONS TO SMOOTH MODULI [J]. | MATHEMATIKA , 2018 , 64 (3) : 701-729 .
MLA Xi, Ping . "TERNARY DIVISOR FUNCTIONS IN ARITHMETIC PROGRESSIONS TO SMOOTH MODULI" . | MATHEMATIKA 64 . 3 (2018) : 701-729 .
APA Xi, Ping . TERNARY DIVISOR FUNCTIONS IN ARITHMETIC PROGRESSIONS TO SMOOTH MODULI . | MATHEMATIKA , 2018 , 64 (3) , 701-729 .
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On triple correlations of Fourier coefficients of cusp forms SCIE Scopus
期刊论文 | 2018 , 183 , 485-492 | JOURNAL OF NUMBER THEORY | IF: 0.684
WoS CC Cited Count: 3 SCOPUS Cited Count: 6
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Abstract :

Assume that alpha, beta are arbitrary arithmetic functions, and that gamma is an arithmetic function, which does not correlate with additive characters. By introducing a simple argument, we are able to give a general upper bound for the triple correlation & para;& para;Sigma(n is an element of(X,2X] alpha(n)beta(n - h)gamma(n + h)& para;& para;averaging over a short variable h. More precise estimates can be obtained by taking gamma to be Fourier coefficients of cusp forms, which improve and stream line the results of Lin and Singh. (C) 2017 Elsevier Inc. All rights reserved.)

Keyword :

Circle method Cusp forms Fourier coefficients Triple correlation

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GB/T 7714 Lu, Guangshi , Xi, Ping . On triple correlations of Fourier coefficients of cusp forms [J]. | JOURNAL OF NUMBER THEORY , 2018 , 183 : 485-492 .
MLA Lu, Guangshi 等. "On triple correlations of Fourier coefficients of cusp forms" . | JOURNAL OF NUMBER THEORY 183 (2018) : 485-492 .
APA Lu, Guangshi , Xi, Ping . On triple correlations of Fourier coefficients of cusp forms . | JOURNAL OF NUMBER THEORY , 2018 , 183 , 485-492 .
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A shifted convolution sum for GL(3) x GL(2) SCIE Scopus
期刊论文 | 2018 , 30 (4) , 1013-1027 | FORUM MATHEMATICUM | IF: 0.867
WoS CC Cited Count: 2 SCOPUS Cited Count: 6
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Abstract :

In this paper, we estimate the shifted convolution sum Sigma(n >= 1) lambda(1)(1, n)lambda(2)(n + h)V(n/x), where Visa smooth function with support in [1, 2], 1 <= vertical bar h vertical bar <= X, and lambda 1 (1, n) and lambda 2(n) are the n-th Fourier coefficients of SL(3, Z) and SL(2, Z) Hecke-Maass cusp forms, respectively. We prove an upper bound 0(X21/22+epsilon), updating a recent result of Munshi.

Keyword :

exponential sums Fourier coefficients of cusp forms Shifted convolution sum

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GB/T 7714 Xi, Ping . A shifted convolution sum for GL(3) x GL(2) [J]. | FORUM MATHEMATICUM , 2018 , 30 (4) : 1013-1027 .
MLA Xi, Ping . "A shifted convolution sum for GL(3) x GL(2)" . | FORUM MATHEMATICUM 30 . 4 (2018) : 1013-1027 .
APA Xi, Ping . A shifted convolution sum for GL(3) x GL(2) . | FORUM MATHEMATICUM , 2018 , 30 (4) , 1013-1027 .
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A quadratic analogue of Titchmarsh divisor problem SCIE Scopus
期刊论文 | 2018 , 184 , 192-205 | JOURNAL OF NUMBER THEORY | IF: 0.684
WoS CC Cited Count: 2 SCOPUS Cited Count: 3
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Abstract :

We consider a quadratic analogue of the classical Titchmarsh divisor problem and prove an upper bound for the average of tau(p(2) + 1) over p <= X. (C) 2017 Elsevier Inc. All rights reserved.

Keyword :

Arithmetic exponent pairs Primes in arithmetic progressions q-Analogue of van der Corput method Titchmarsh divisor problem

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GB/T 7714 Xi, Ping . A quadratic analogue of Titchmarsh divisor problem [J]. | JOURNAL OF NUMBER THEORY , 2018 , 184 : 192-205 .
MLA Xi, Ping . "A quadratic analogue of Titchmarsh divisor problem" . | JOURNAL OF NUMBER THEORY 184 (2018) : 192-205 .
APA Xi, Ping . A quadratic analogue of Titchmarsh divisor problem . | JOURNAL OF NUMBER THEORY , 2018 , 184 , 192-205 .
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How strong can primes be SCIE Scopus
期刊论文 | 2017 , 179 (4) , 363-373 | ACTA ARITHMETICA | IF: 0.476
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Keyword :

Brun-Titchmarsh theorem greatest prime factor strong primes

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GB/T 7714 Xi, Ping . How strong can primes be [J]. | ACTA ARITHMETICA , 2017 , 179 (4) : 363-373 .
MLA Xi, Ping . "How strong can primes be" . | ACTA ARITHMETICA 179 . 4 (2017) : 363-373 .
APA Xi, Ping . How strong can primes be . | ACTA ARITHMETICA , 2017 , 179 (4) , 363-373 .
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