Weak subconvexity for central values of $L$-functions

By Kannan Soundararajan. 2008

69 citations recorded by the source corpus.

We describe a general method to obtain weak subconvexity bounds for many classes of $L$-functions. This has applications to a conjecture of Rudnick and Sarnak for the mass equidistribution of Hecke eigenforms (see arxiv.org:math/0809.1636).

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/77dcf1d3cc31e9093771ecc3de19b74878bd5d2c

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In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

Distribution of periodic torus orbits and Duke's theorem for cubic fields (2007, background): “Soundararajan [41] proved a very general weak subconvex bound, valid for a wide class of L-functions.”
Mass equidistribution for Hecke eigenforms (2008, background): “em 3 (i) shows that hφFk,Fki is small. This shows how Theorems 2 and 3 complement each other in the cusp form case. In the case of Eisenstein series, we ﬁrst show how the weak subconvexity results in [17] lead to a satisfactory bound for the term Rk(f) appearing in Theorem 2 (ii) (see Lemma 1 below)”
Equidistribution Of Cusp Forms In The Level Aspect (2010, methodology): “)(1−βp−1/2)(1+αp−1/2)(1+βp−1/2) (1−α2p−1)(1−p−1)(1 −β2p−1) = p−1, as asserted.22 PAUL D. NELSON 5. ProofofTheorem 1.3 We combine Theorem 3.1 and Theorem 4.1 with Soundararajan’s weak subconvex bounds [39] to complete the proof of Theorem 1.3. Fix a positive even integer k. Let fbe a newform of weigh”
Weak subconvexity without a Ramanujan hypothesis (2018, background): “3 extends considerably the class of L-functions for which a weak subconvexity bound may be established, but the power of logC(π) saved is smaller than in [28].”
The orbit method and analysis of automorphic forms (2018, background): “is roughly the fourth power of the analytic conductor of the relevant L-function. By ignoring all but one term and slowly shrinking the family, we obtain L( ;) = o cond( ) 1=4 (1.4) (compare with [91, 90]). The hypotheses relevant for (1.4) are that is ﬁxed, while traverses a sequence whose archim”