TY - BOOK

T1 - Investigating slopes of overconvergent modular forms

AU - Destefano, Dino

PY - 2017

Y1 - 2017

N2 - We study the slopes of the Atkin’s U operator acting on overconvergent p-adic modular forms. In the case of tame level 1 and for p =5,7,13; we compute a quadratic lower bound for the Newton polygon of U. The methods of proof are explicit and rely on a certain deformation of the U operator and its characteristic power series.This gives us the possibility to compute the smallest possible slope for p=5,7 and to prove necessary and sufficient conditions on the weight such that the dimension of the cuspidal space is one. This result allows us to exhibit some p-adic analytic families of modular forms in the framework of Coleman’s theory.We then formulate a conjecture that would allow us to extend our analysis to all the congruence classes modulo p−1.

AB - We study the slopes of the Atkin’s U operator acting on overconvergent p-adic modular forms. In the case of tame level 1 and for p =5,7,13; we compute a quadratic lower bound for the Newton polygon of U. The methods of proof are explicit and rely on a certain deformation of the U operator and its characteristic power series.This gives us the possibility to compute the smallest possible slope for p=5,7 and to prove necessary and sufficient conditions on the weight such that the dimension of the cuspidal space is one. This result allows us to exhibit some p-adic analytic families of modular forms in the framework of Coleman’s theory.We then formulate a conjecture that would allow us to extend our analysis to all the congruence classes modulo p−1.

UR - https://soeg.kb.dk/permalink/45KBDK_KGL/fbp0ps/alma99122488153505763

M3 - Ph.D. thesis

BT - Investigating slopes of overconvergent modular forms

PB - Department of Mathematical Sciences, Faculty of Science, University of Copenhagen

ER -