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

By Xiannan Li. 2009

122 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Artificial Intelligence, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a2515a067a49498a2e7fd01adeb4d87a2b3fcb04

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In Algebra and Number Theory

In Artificial Intelligence

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Citations in the corpus

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The horocycle flow at prime times (2011, methodology): “Instead we again exploit the average over k and again we use [26]; for x ≥ 1”
Nodal Domains of Maass Forms I (2012, methodology): “i03] that sym4(f) corresponds to an automorphic cusp form on GL 5, and then applies Molteni’s extension [Mo02] to GL n of Iwaniec’s method to bound sums of Fourier coefﬁcients of cusp forms (see also [Li10], and [LY11] where a similar result is proved for k =4). For the proofs of some of the theorem”
The quantum unique ergodicity conjecture for thin sets (2013, methodology): “ctral large sieve inequality shows (5.67) X tj≤V X n≤N anλj(n) 2 ≪ (VN)ε(V2 +N) X n≤N |an|2. In our application, we have P n≤N |A(1,n)|2 n ≪ (NT)ε by the convexity bound for RankinSelberg L-functions [Li]. 6. The geodesicQUEtheorem for Eisensteinseries Here we present the proof of our main result, T”