"This book discusses the p-adic modular forms, the eigencurve that parameterize them, and the p-adic L-functions one can associate to them. These theories and their generalizations to automorphic forms for group of higher ranks are of fundamental importance in number theory. For…
The theory of complex dynamics in one variable, initiated by Fatou and Julia in the early twentieth century, concerns the iteration of a rational function acting on the Riemann sphere. Building on foundational investigations of p-adic dynamics in the late twentieth century, dyna…
The Berkovich Line over Z This text is devoted to the study of the Berkovich line over the ring of integers of a number field. It is a geometric object which naturally contains complex analytic lines (or their quotient by conjugation), associated to the infinite places, and clas…
"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 e…
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 ex…
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 ex…
"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 e…
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