Families of L-Functions and Their Symmetry

Peter Sarnak, Sug Woo Shin, Nicolas Templier

Type: Book-Chapter

Publication Date: 2016-01-01

Citations: 47

DOI: https://doi.org/10.1007/978-3-319-41424-9_13

Abstract

A few years ago the first-named author proposed a working definition of a family of automorphic L-functions. Then the work by the second and third-named authors on the Sato–Tate equidistribution for families made it possible to give a conjectural answer for the universality class introduced by Katz and the first-named author for the distribution of the zeros near s = 1/2. In this article we develop these ideas fully after introducing some structural invariants associated to the arithmetic statistics of a family.

Locations

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arXiv (Cornell University) - PDF
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arXiv (Cornell University) - PDF

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Works Cited by This (114)

Action	Title	Year	Authors
+	None	2003	Farrell Brumley
+	Some Contemporary Problems with Origins in the Jugendtraum	2001	R. P. Langlands
+	Sato-Tate equidistribution for families of Hecke-Maass forms on SL(n,R)/SO(n)	2015	Jasmin Matz Nicolas Templier
+	The Geometry and Cohomology of Some Simple Shimura Varieties.	2001	Michael Harris Richard Taylor Vladimir G. Berkovich
+	Weyl's law for Hecke operators on GL(n) over imaginary quadratic number fields	2013	Jasmin Matz
+	Lectures on N[x](p)	2012	Jean-Pierre Serre
+ PDF	Zeta Functions of Simple Algebras	1972	Roger Godement Hervé Jacquet
+ PDF	Random Matrices, Frobenius Eigenvalues, and Monodromy	1998	Nicholas M. Katz Peter Sarnak
+	The average size of the 5-Selmer group of elliptic curves is 6, and the average rank is less than 1	2013	Manjul Bhargava Arul Shankar
+	Applications of sieve methods to the theory of numbers	1976	C. Hooley