English

A note on the zeroes of the Fredholm series

Complex Variables 2024-04-09 v2 Number Theory

Abstract

The issue had been raised whether the Fredholm series z+z2+...+z2n+...z+z^2+...+z^{2^n}+... has infinitely many zeroes in the unit disk. We provide an affirmative answer, proving that in fact every complex number occurs as a value infinitely many times.

Keywords

Cite

@article{arxiv.2006.11922,
  title  = {A note on the zeroes of the Fredholm series},
  author = {Umberto Zannier and Francesco Veneziano},
  journal= {arXiv preprint arXiv:2006.11922},
  year   = {2024}
}

Comments

By Umberto Zannier, with an appendix by Francesco Veneziano