Bulletin of the London Mathematical Society Advance Access originally published online on October 29, 2008
Bulletin of the London Mathematical Society 2008 40(6):1081-1090; doi:10.1112/blms/bdn094
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© 2008 London Mathematical Society
Bounds for the coefficients of powers of the
-function
Department of Mathematics
University of Illinois
Urbana, IL 61801
USA
Received 30 October 2007. Revision received 1 April 2008.
For k
1, let
. It follows from Deligne's proof of the Weil conjectures that there is a constant Ck so that |
k(n)|
Ck d(n) n(12k–1)/2. We study the value of Ck as a function of k, and show that it tends to zero very rapidly.
2000 Mathematics Subject Classification 11F30 (primary), 11F67 (secondary).