5 papers
Towards Keating-Snaith's conjecture for cubic Hecke -functions over the Eisenstein field
Hua Lin, Peng-Jie Wong
A famous conjecture of Keating and Snaith asserts that central values of -functions in a given family admit a log-normal distribution with a prescribed mean and variance dependi…
Square-free orders for CM elliptic curves modulo in short intervals
Peng-Jie Wong
Let be a CM elliptic curve over . We refine the work of Cojocaru on the asymptotic formulae for the number of primes for which the reduction modulo of …
New zero-free regions for Dedekind zeta-functions at small and large ordinates
Sourabhashis Das, Swati Gaba, Ethan Simpson Lee +2
Given a number field , we obtain new and explicit zero-free regions for Dedekind zeta-functions of , which refine the previous works of Ahn--Kwon, Kadiri, and…
Low-Lying Zeros of -functions of Adélic Hilbert Modular Forms and their Convolutions
Alia Hamieh, Peng-Jie Wong
In this article, we study the density conjecture of Katz and Sarnak for -functions of adélic Hilbert modular forms and their convolutions. In particular, under the generalised…
On distributions of -values and orders of Sha groups in families of quadratic twists
Peng-Jie Wong
In this article, we aim to establish a prototype result regarding lower bounds of (joint) distributions of central -values through extending a method of Radziwill and Soundarar…