Small gaps between zeros of twisted L-functions

Unnormalized Differences between Zeros of L-functions

We study a subtle inequity in the distribution of unnormalized differences between imaginary parts of zeros of the Riemann zeta function, which was observed by a number of authors. We establish a precise measure which explains the phenomenon, that the location of each Riemann zero is encoded in the distribution of large Riemann zeros. We also extend these results to zeros of more general L-func...

Marco’s Repulsion Phenomenon between Zeros of L-functions

We study a subtle inequity in the distribution of differences between imaginary parts of zeros of the Riemann zeta function. We establish a precise measure which explains the phenomenon, first observed by R. P. Marco, that the location of each Riemann zero is encoded in the distribution of large Riemann zeros. We also extend these results to zeros of more general L-functions. In particular, we ...

Twisted Symmetric-square L-functions and the Nonexistence of Siegel Zeros on Gl(3)

§

Twisted L-Functions and Monodromy

Superposition of zeros of distinct L-functions

In this paper we ®rst prove a weighted prime number theorem of an ``o ̈-diagonal'' type for Rankin-Selberg L-functions of automorphic representations of GLm and GLm 0 over Q. Then for m ˆ 1, or under the Selberg orthonormality conjecture for mV 2, we prove that nontrivial zeros of distinct primitive automorphic L-functions for GLm over Q are uncorrelated, for certain test functions whose Fourier...