Perspectives on the Analytic Theory of L-Functions

By Henryk Iwaniec, Peter Sarnak. 2000

266 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c34b6b62dfb6710253532b18c2b885b26a7c7233

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Citations in the corpus

The subconvexity problem for Artin L–functions (2002, background): “For a survey with references on the general subconvexity problem for L-functions see [ IS ].”
The subconvexity problem for GL2 (2009, background): “The subconvexity problem is concerned with the size of L(π, s) when <s = 1/2: it consists in improving over the so-called convexity bound (see [37] for instance) L(π, 1/2) n,F,ε C(π) for any(1) ε > 0.”
Distribution of periodic torus orbits and Duke's theorem for cubic fields (2007, background): “The first bound in (4) is called a subconvex bound and is due to Duke, Friedlander and Iwaniec [15]; it is a special instance of the so-called subconvexity problem for automorphic L-functions (see [ 35 ] for a discussion of that problem).”
Mass equidistribution for Hecke eigenforms (2008, background): “N T ] 9 S ep 2 00 8 MASS EQUIDISTRIBUTION FOR HECKE EIGENFORMS”
Sub-Weyl subconvexity for Dirichlet $L$-functions to prime power moduli (2014, background): “For an automorphic representation π of GL(n), the statement that (2) |L(1/2, π)| ≪ C(π)θ+ǫ, where C(π) is the analytic conductor of π as defined by Iwaniec and Sarnak [13] and θ = 14 , is known as the convexity bound and follows from the basic analytic properties of L(s, π).”
Families of L -Functions and Their Symmetry (2014, background): “Other examples are the GL2 subconvexity results which are proved by deforming the given form in a family (see [57] and [78] for accounts).”
Upper and lower bounds at s = 1 for certain Dirichlet series with Euler product (2002, background): “, the product of the level N and the eigenvalue λ; and in general, for the L-functions associated with cuspidal automorphic representations of the groups GL(d), R is of the order of the analytic conductor introduced by Iwaniec and Sarnak in [13].”
Rankin-Selberg $L$-functions in the level aspect (2002, background): “One important challenge in the theory ofL functions is to provide upper bounds for their values on the critical line, in particular to improve, by a positive exponent, the “convexity” bound arising from the Phragmen-Lindel¨ of principle (see [ IS2 ] for a motivating introduction to these questions).”
Subconvexity bounds for triple L-functions and representation theory (2006, methodology): “We refer to [IS] for a discussion of the subconvexity problem which is at the core of modern analytic number theory.”
Riemann's zeta function and beyond (2003, unknown): “This is because both s(s− 1)π−s/2Γ(s/2)ζ(s) and 1sΓ(s/2) are entire and of order 1 (Theorem 2.1).”