Upper bounds on L-functions at the edge of the critical strip

Details Upper bounds on L-functions at the edge of the critical strip Upper bounds on L-functions at the edge of the critical strip

2009-04-06

arxiv.org/abs/0904.0850v5

Mathematics

Number Theory

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Scientific paper

The problem of finding upper bounds for L-functions at the edge of the critical strip has a long and interesting history. Here, the situation for classical L-functions such as Dirichlet L-functions is relatively well understood. The reason for this is because the size of the coefficients of these L-functions is known to be small. Although L-functions are generally expected to have coefficients which are bounded by a constant at the primes, this has only been proven for a small class of familiar examples. Our main focus here is on the problem of finding upper bounds for L-functions for which we have comparatively bad bounds for the size of the coefficients.

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