4 citations · 11 across the 10 of their papers we have counts for
7 papers · 1 filter
The first moment of primitive quartic \(L\)-functions with a secondary term
Ziwei Hong, Zhiyong Zheng
Let be a fixed odd prime power. We study the first moment of central values of primitive quartic Dirichlet -functions over $\F_q[T]$, with fixed genus and w…
The second moment of Ramanujan sums
Hong Ziwei, Zheng Zhiyong
In this paper, we study , the second moment of Ramanujan sums. Assuming the Riemann Hypothesis(RH), we establish an asymptotic formula for with improved error te…
On the High Dimensional RSA Algorithm -- A Public Key Cryptosystem Based on Lattice and Algebraic Number Theory
Zhiyong Zheng, Fengxia Liu
The most known of public key cryptosystem was introduced in 1978 by Rivest, Shamir and Adleman [19] and now called the RSA public key cryptosystem in their honor. Later, a few auth…
Simultaneous Diophantine Approximation in Function Fields
Zhiyong Zheng
There are abundant results on Diophantine approximation over fields of positive characteristic (see the survey papers [13, 25]), but there is very little information about simultan…
On the Polynomial Ramanujan Sums over Finite Fields
Zhiyong Zheng
The polynomial Ramanujan sum was first introduced by Carlitz [7], and a generalized version by Cohen [10]. In this paper, we study the arithmetical and analytic properties of these…
Davenport-Hasse's Theorem for Polynomial Gauss Sums over Finite Fields
Zheng Zhiyong
In this paper, we study the polynomial Gauss sums over finite fields, and present an analogue of Davenport-Hasse's theorem for the entire polynomial Gauss sums, which is a generali…
On the distribution of Jacobi sums
Qing Lu, Weizhe Zheng, Zhiyong Zheng
Let be a finite field of elements. For multiplicative characters of , we let denote the Jacobi sum. Nic…