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

Abstract

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.

arXiv commentFinal version

References in corpus (2)

• Moments of the Riemann zeta-function
• Mass equidistribution for Hecke eigenforms

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• Applications of analytic newvectors for $\mathrm{GL}(n)$
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• Towards a ${\mathrm{GL}}_n$ variant of the Hoheisel phenomenon
• Zeros of Rankin-Selberg $L$-functions in families
• The second moment of $\mathrm{GL}(n)\times \mathrm{GL}(n)$ Rankin--Selberg $L$-functions
• A Density Theorem for $\mathrm{Sp}(4)$
• Dirichlet twists of ${\mathrm{GL}}_n$-automorphic $L$-functions and hyper-Kloosterman Dirichlet series