On the uniform distribution of the zero ordinates of the $L-$function associated with $\theta(z)^{-3}\,\eta(2z)^{12}$

TL;DR

This paper proves that the imaginary parts of zeros of specific L-functions related to half-integral weight cusp forms are evenly spread across the unit interval, indicating a uniform distribution pattern.

Contribution

It establishes the uniform distribution of zero ordinates for a class of L-functions associated with half-integral weight cusp forms, a novel result in the field.

Findings

Zeros are uniformly distributed modulo one.

Supports conjectures about zero distributions of L-functions.

Advances understanding of half-integral weight cusp form L-functions.

Abstract

We show that the ordinates of the nontrivial zeros of certain $L-$functions attached to half-integral weight cusp forms are uniformly distributed modulo one.