China University of Mining and Technology

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19952020

most citedNonlinear Schrödinger Equation: Generalized Darboux Transformation and Rogue Wave Solutions

982 citations

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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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8 papers · 1 filter

math.NT2020

Average of Hardy's function at Gram points

Xiaodong Cao, Yoshio Tanigawa, Wenguang Zhai

Let $Z (t) = χ^{- 1/2} (1/2 + i t) ζ (1/2 + i t) = e^{i θ (t)} ζ (1/2 + i t)$ be Hardy's function and $g (n)$ be the $n$ -th Gram points defined by $θ (g (n)) = π n$ . Titchmarsh proved that $\sum_{n \leq N} Z(…

math.NT2020

Some mean value results related to Hardy's function

Xiaodong Cao, Yoshio Tanigawa, Wenguang Zhai

Let $ζ (s)$ and $Z (t)$ be the Riemann zeta function and Hardy's function respectively. We show asymptotic formulas for $\int_{0}^{T} Z (t) ζ (1/2 + i t) d t$ and $\int_{0}^{T} Z^{2} (t) ζ (1/2 + i t) d t$ .…

math.NT2017★ 11 cited

On multivariable averages of divisor functions

László Tóth, Wenguang Zhai

We deduce asymptotic formulas for the sums $\sum_{n_{1}, \dots, n_{r} \leq x} f (n_{1} \dots n_{r})$ and $\sum_{n_{1}, \dots, n_{r} \leq x} f ([n_{1} \dots n_{r}])$ , where $r \geq 2$ is a fixed integer, $[n…

math.NT2017

On the Fourth Power Moment of Fourier Coefficients of Cusp Form

Jinjiang Li, Panwang Wang, Min Zhang

Let $a (n)$ be the Fourier coefficients of a holomorphic cusp form of weight $κ = 2 n ⩾ 12$ for the full modular group and $A (x) = n ⩽ x \sum a (n)$ . In this paper, w…

math.NT2016

Hua's Theorem with the Primes in Piatetski-Shapiro Prime Sets

Jinjiang Li, Min Zhang

In this paper, we study the hybrid problem of Hua's theorem and the Piatetski-Shapiro prime number theorem, and obtain results in this direction of the nonhomogeneous case $k = 3$ , w…

math.NT2016★ 1 cited

On Two Diophantine Inequalities Over Primes

Min Zhang, Jinjiang Li

Let $1 < c < 37/18, c \neq = 2$ and $N$ be a sufficiently large real number. In this paper, we prove that, for almost all $R \in (N, 2 N],$ the Diophantine inequality $|p_1^c+p_2^c+p_3^c-R|<\…

math.NT2016★ 1 cited

A Weighted Divisor Problem

Lirui Jia, Wenguang Zhai

We study a weighted divisor function $mn \leq x \sum^{'} cos (2 π m θ_{1}) sin (2 π n θ_{2})$ , where $θ_{i} (0 < θ_{i} < 1)$ is a rational number. By connecting it with the divisor pro…

math.NT2015★ 9 cited

On the Tong-type identity and the mean square of the error term for an extended Selberg class

Xiaodong Cao, Yoshio Tanigawa, Wenguang Zhai

In 1956, Tong established an asymptotic formula for the mean square of the error term in the summatory function of the Piltz divisor function $d_{3} (n) .$ The aim of this paper is to…