A Look at Chowla's Problem

TL;DR

This paper reviews the historical context and key results related to Chowla's problem on solutions to L(1,f)=0 for periodic functions, highlighting recent advances that provide a complete solution.

Contribution

It synthesizes classical and recent findings, offering a comprehensive overview of the problem and its resolution when recent results are combined with earlier work.

Findings

Baker, Birch, and Wirsing established foundational results.

Recent work by Chatterjee, Murty, and Pathak completes the solution.

The paper clarifies the conditions under which L(1,f)=0 solutions exist.

Abstract

In this paper we look at the history behind Chowla's problem on the solutions to $L(1,f) = 0$ for periodic $f$. We focus on the results given by Baker, Birch and Wirsing on the topic. We briefly discuss recent results due to Chatterjee, Murty and Pathak which give a full solution when combined with the work of Baker, Birch and Wirsing.