William D. Banks

activity

20242026

collaborators

4 papers

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 $D (s) = \sum_{n \geq 1} ζ (2 n) n^{- s}$ , which continues meromorphically to $C$ w…

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 $L (s, χ_{0})$ . At…

math.HO2025

The alien in the Riemann zeta function

William D. Banks

In space, no one can hear you scream.

math.NT2024

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…

Zeros of the Dirichlet series of even zeta values

Unshared zeros of Dirichlet L-functions

The alien in the Riemann zeta function

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

Unshared zeros of Dirichlet $L$ -functions