William D. Banks

works on

pair correlation 1 poisson statistics 1 random matrix theory 1 riemann zeta function 1 zero ordinates 1

From the 1 of 5 linked papers with an AI index.

collaborators

5 papers

math.NT2026

Unshared zeros of Dirichlet $L$ -functions

William Banks, Kyle Loftus

We prove that no Dirichlet $L$ -function (and more generally, no nontrivial finite linear combination of Dirichlet $L$ -functions) can vanish at every zero of a fixed $L (s, I ¨ _{0})$ . At…

math.NT2026

Zeros of the Dirichlet series of even zeta values

William D. Banks

We give a complete unconditional description of the zero set of the Dirichlet series $D (s) := \sum_{n \geq 1} I^¶ (2 n) n^{- s}$ , which continues meromorphically to $C$ with a…

math.NT2026

Pair correlation for sums of two ordinates of zeros of the Riemann zeta function

William D. Banks

Assuming the Riemann Hypothesis, the paper extends Montgomery's pair correlation method to analyze the distribution of differences between sums of two ordinates of nontrivial zeros…

math.NT2025

A variant of the Linnik-Sprindzuk theorem for simple zeros of Dirichlet L-functions

William D. Banks

For a primitive Dirichlet character $X$ , a new hypothesis $R H_{s im}^{†} [X]$ is introduced, which asserts that (1) all simple zeros of $L (s, X)$ in the critical strip are located…

math.HO2025

The alien in the Riemann zeta function

William D. Banks

In space, no one can hear you scream.

Unshared zeros of Dirichlet L-functions

Zeros of the Dirichlet series of even zeta values

Pair correlation for sums of two ordinates of zeros of the Riemann zeta function

A variant of the Linnik-Sprindzuk theorem for simple zeros of Dirichlet L-functions

The alien in the Riemann zeta function

Unshared zeros of Dirichlet $L$ -functions