Families of L -Functions and Their Symmetry

By Peter Sarnak, S. Shin, Nicolas Templier. 2014

66 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4e8ca4c4cba481afccdfd9eba4e3ba67c7ad7656

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In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

The orbit method and analysis of automorphic forms (2018, background): “One may see this by, for instance, considering the analogous situation with the number field replaced by a function field (see also [89, 85]).”
The fourth moment of Dirichlet L-functions along a coset and the Weyl bound (2019, methodology): “be stated in terms of subsets of the local unitary duals ̂ GL2(Qv), and so our definition fits into the framework of harmonic families of [SST].”
On ℓ-torsion in class groups of number fields (2016, result): “Our counting theorems improve upon analogous results that appear in four recent papers, three [Yan09, CK15, SST15b] in the area of finding symmetry groups of families of L-functions (see [SST15a] for a general overview of the area) and one [OT14] studying the distribution of ramified primes in small”