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arXiv:math/0506218 [math.NT]AbstractReferencesReviewsResources

The maximum size of $L$-functions

David W. Farmer, S. M. Gonek, C. P. Hughes

Published 2005-06-11, updated 2006-08-03Version 3

We conjecture the true rate of growth of the maximum size of the Riemann zeta function and other $L$-functions. We support our conjecture using arguments from random matrix theory, conjectures for moments of $L$-functions, and also by assuming a random model for the primes.

Comments: Final version. To appear in Crelle
Categories: math.NT
Subjects: 11M26
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