The Second Moment Theory of Families of L-functions-the Case of Twisted Hecke L-functions - Brossura

Blomer, Valentin; Kowalski, Emmanuel; Michel, Philippe G.; Milicevic, Djordje; Sawin, Will

 
9781470456788: The Second Moment Theory of Families of L-functions-the Case of Twisted Hecke L-functions
Brossura
ISBN 10: 1470456788 ISBN 13: 9781470456788
Casa editrice: Amer Mathematical Society, 2023

Sinossi

"For a fairly general family of L-functions, we survey the known consequences of the existence of asymptotic formulas with power-saving error term for the (twisted) first and second moments of the central values in the family. We then consider in detail the important special case of the family of twists of a fixed cusp form by primitive Dirichlet characters modulo a prime q, and prove that it satisfies such formulas. We derive arithmetic consequences: a positive proportion of central values L(f [circled x] X, 1/2) are non-zero, and indeed bounded from below; there exist many characters X for which the central L-value is very large; the probability of a large analytic rank decays exponentially fast. We finally show how the second moment estimate establishes a special case of a conjecture of Mazur and Rubin concerning the distribution of modular symbols"--

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Editore
Amer Mathematical Society
Data di pubblicazione
2023
Lingua
Inglese
ISBN 10 
1470456788
ISBN 13 
9781470456788
Rilegatura
Copertina flessibile
Numero di pagine
154
Contatto del produttore
non disponibile
Persona responsabile
non disponibile