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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 {Delta}-function

Jeremy Rouse

Department of Mathematics
University of Illinois
Urbana, IL 61801
USA

Received 30 October 2007. Revision received 1 April 2008.

For k≥1, let Formula . It follows from Deligne's proof of the Weil conjectures that there is a constant Ck so that | {tau}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).


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