Nathan Ng

THE DIOPHANTINE EQUATION A4 + 2δB2 = Cn

In a previous paper, the second author proved that the equation had no integral solutions for prime p > 211 and (A,B,C) = 1. In the present paper, we explain how to extend this result to smaller exponents, and to the related equation

A note on the gaps between consecutive zeros of the Riemann zeta-function

Assuming the Riemann Hypothesis, we show that infinitely often consecutive non-trivial zeros of the Riemann zeta-function differ by at most 0.5155 times the average spacing and that infinitely often they differ by at least 2.6950 times the average spacing.

Simple zeros of modular L-functions

Assuming the generalized Riemann hypothesis, we prove quantitative estimates for the number of simple zeros on the critical line for the L-functions attached to classical holomorphic newforms.

NONZERO VALUES OF DIRICHLET L-FUNCTIONS IN VERTICAL ARITHMETIC PROGRESSIONS

Let

LIMITING DISTRIBUTIONS OF THE CLASSICAL ERROR TERMS OF PRIME NUMBER THEORY

L(s,chi)

Explicit zero density theorems for Dedekind zeta functions

be a fixed Dirichlet

Lower Bounds for Moments of ζ′(ρ)

L

A note on a conjecture of Gonek

-function. Given a vertical arithmetic progression of

Subconvexity for modular form L-functions in the t aspect

T

Lower bounds for moments of zeta prime rho

points on the line