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The maximum size of $L$-functions

David W. Farmer·S. M. Gonek·C. P. Hughes
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Abstract

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.

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David W. Farmer, S. M. Gonek, C. P. Hughes. 2006-08-03. The maximum size of $L$-functions. https://arxiv.org/abs/math/0506218

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