Supersingular p-adic L-functions, Maass-Shimura operators and Waldspurger formulas / Daniel J. Kriz.

"A groundbreaking contribution to number theory that unifies classical and modern results This book develops a new theory of p -adic modular forms on modular curves, extending Katz's classical theory to the supersingular locus. The main novelty is to move to infinite level and extend coefficients to...

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Bibliographic Details
Uniform Title:Annals of mathematics studies ; no. 212.
Main Author: Kriz, Daniel J. (Author)
Language:English
Published: Princeton : Princeton University Press, 2021.
Series:Annals of mathematics studies ; no. 212.
Subjects:
Number theory.
p-adic analysis.
L-functions.
Physical Description:xiii, 258 pages : illustrations ; 24 cm.
Format: Book
Contents:
  • Introduction
  • Preliminaries: Generalities
  • Preliminaries: Geometry of the infinite-level modular curve
  • The fundamental de Rham periods
  • The p-adic Maass-Shimura operator
  • p-adic analysis of the p-adic Maass-Shimura operators
  • Bounding periods at supersingular CM points
  • Supersingular Rankin-Selberg p-adic L-functions
  • The p-adic Waldspurger formula.