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On a Conjecture of Chowla and Milnor
  Published:2011-06-25
 Printed: Dec 2011
Canadian Journal of Mathematics
  • 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
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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, 11F11 show english descriptions Dedekind eta function, Dedekind sums
Holomorphic modular forms of integral weight 11F20 - Dedekind eta function, Dedekind sums
11F11 - Holomorphic modular forms of integral weight
 
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