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# On a Conjecture of Chowla and Milnor

Published:2011-06-25
Printed: Dec 2011
• Sanoli Gun,
The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
• M. Ram Murty,
Department of Mathematics, Queen's University, Kingston, ON K7L 3N6, Canada
• Purusottam Rath,
Chennai Mathematical Institute, Plot No H1, SIPCOT IT Park, Padur PO, Siruseri 603103, Tamil Nadu, India
 Format: LaTeX MathJax

## Abstract

In this paper, we investigate a conjecture due to S. and P. Chowla and its generalization by Milnor. These are related to the delicate question of non-vanishing of $L$-functions associated to periodic functions at integers greater than $1$. We report on some progress in relation to these conjectures. In a different vein, we link them to a conjecture of Zagier on multiple zeta values and also to linear independence of polylogarithms.
 MSC Classifications: 11F20 - Dedekind eta function, Dedekind sums 11F11 - Holomorphic modular forms of integral weight