PENG-JIE Wong

activity

20192023

most citedShifted moments of the Riemann zeta function

7 citations · 10 across the 8 of their papers we have counts for

collaborators

11 papers

math.NT2023

Cyclicity and exponent of elliptic curves modulo $p$ in arithmetic progressions

Peng-Jie Wong

In this article, we study the cyclicity problem of elliptic curves $E / Q$ modulo primes in a given arithmetic progression. We extend the recent work of Akbal and Güloğlu by pr…

math.NT2022★ 7 cited

Shifted moments of the Riemann zeta function

Nathan Ng, Quanli Shen, Peng-Jie Wong

In this article, we prove that the Riemann hypothesis implies a conjecture of Chandee on shifted moments of the Riemann zeta function. The proof is based on ideas of Harper concern…

math.NT2022★ 1 cited

The eighth moment of the Riemann zeta function

Nathan Ng, Quanli Shen, Peng-Jie Wong

In this article, we establish an asymptotic formula for the eighth moment of the Riemann zeta function, assuming the Riemann hypothesis and a quaternary additive divisor conjecture…

math.NT2022

Refinements of strong multiplicity one for $GL (2)$

Peng-Jie Wong

For distinct unitary cuspidal automorphic representations $π_{1}$ and $π_{2}$ for $GL (2)$ over a number field $F$ and any $α \in R$ , let $S_{α}$ be the set of prim…

math.NT2021

Counting zeros of the Riemann zeta function

Elchin Hasanalizade, Quanli Shen, Peng-Jie Wong

In this article, we show that $N (T) - \frac{T}{2 π} lo g (\frac{T}{2 π e}) \leq 0.1038 lo g T + 0.2573 lo g lo g T + 9.3675$ where $N (T)$ denotes the n…

math.NT2021★ 2 cited

Primes in the Chebotarev density theorem for all number fields

Habiba Kadiri, Peng-Jie Wong

We establish an explicit bound for the least prime occurring in the Chebotarev density theorem without any restriction. Let $L / K$ be any Galois extension of number fields such that…

math.NT2021

Fourier coefficients of automorphic $L$ -functions over primes in ray classes

Amir Akbary, Peng-Jie Wong

We prove Siegel-Walfisz type theorems (over long and short intervals) for the Fourier coefficients of certain automorphic $L$ -functions and Rankin-Selberg $L$ -functions over number…

math.NT2021

Counting zeros of Dedekind zeta functions

Elchin Hasanalizade, Quanli Shen, Peng-Jie Wong

Given a number field $K$ of degree $n_{K}$ and with absolute discriminant $d_{K}$ , we obtain an explicit bound for the number $N_{K} (T)$ of non-trivial zeros (counted with multiplicity),…

math.NT2020

Almost all primes satisfy the Atkin-Serre conjecture and are not extremal

Ayla Gafni, Jesse Thorner, Peng-Jie Wong

Let $f (z) = \sum_{n = 1}^{\infty} a_{f} (n) e^{2 π in z}$ be a non-CM holomorphic cupsidal newform of trivial nebentypus and even integral level $k \geq 2$ . Deligne's proof of the Weil conje…

math.NT2019

On the moments of torsion points modulo primes and their applications

Amir Akbary, Peng-Jie Wong

Let $A [n]$ be the group of $n$ -torsion points of a commutative algebraic group $A$ defined over a number field $F$ . For a prime ideal $p$ , we let $N_{\…

math.NT2019

The least prime ideal in the Chebotarev Density Theorem

Habiba Kadiri, Nathan Ng, Peng-Jie Wong

In this article, we prove a new bound for the least prime ideal in the Chebotarev density theorem, which improves the main theorem of Zaman [Funct. Approx. Comment. Math. 57 (2017)…

Cyclicity and exponent of elliptic curves modulo p in arithmetic progressions

Shifted moments of the Riemann zeta function

The eighth moment of the Riemann zeta function

Refinements of strong multiplicity one for GL(2)

Counting zeros of the Riemann zeta function

Primes in the Chebotarev density theorem for all number fields

Fourier coefficients of automorphic L-functions over primes in ray classes

Counting zeros of Dedekind zeta functions

Almost all primes satisfy the Atkin-Serre conjecture and are not extremal

On the moments of torsion points modulo primes and their applications

The least prime ideal in the Chebotarev Density Theorem

Cyclicity and exponent of elliptic curves modulo $p$ in arithmetic progressions

Refinements of strong multiplicity one for $GL (2)$

Fourier coefficients of automorphic $L$ -functions over primes in ray classes