The maximum size of $L$-functions

Mathematics – Number Theory

Scientific paper

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Final version. To appear in Crelle

Scientific paper

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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