Location of the zeros of certain cuspforms

Abstract

In this note, we prove a conjecture of Reitzes, Vulakh and Young on the location of the zeros of certain cuspforms of level one.

Interlacing of Zeros of Eisenstein Series

“…Expanding on Nozaki's method, in a previous paper [Gri21] we proved that the nontrivial zero of E k (e iθ ) closest to π/2 is distinct from any non-trivial zero of E (e iθ ) for k > , and conjectured that all non-trivial zeros of E k (e iθ ) are distinct from all non-trivial zeros of E (e iθ ) for any = k. In this paper, we further refine Nozaki's methods and extend the results of our previous paper to prove Theorem 1.1, which establishes necessary and sufficient conditions under which the non-trivial zeros of E k (e iθ ) and E (e iθ ) interlace. We also want to point out that the result obtained in this paper has been applied in [XZ21] to study the location of zeros of certain cuspforms.…”