Supersingular p-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas

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 period sheaves coming from relative p -adic Hodge theory. This makes it possible to trivialize the Hodge bundle on the infinite-level modular curve by a "canonical differential" that restricts to the