p-Adic Aspects of Modular Forms

The aim of this book is to give a systematic exposition of results in some important cases where p-adic families and p-adic L-functions are studied. We first look at p-adic families in the following cases: general linear groups, symplectic groups and definite unitary groups. We also look at applications of this theory to modularity lifting problems. We finally consider p-adic L-functions for GL(2), the p-adic adjoint L-functions and some cases of higher GL(n).

Contents:

• An Overview of Serre's p-Adic Modular Forms (Miljan Brakočević and R Sujatha)
• p-Adic Families of Ordinary Siegel Cusp Forms (Jacques Tilouine)
• Ordinary Families of Automorphic Forms on Definite Unitary Groups (Baskar Balasubramanyam and Dipramit Majumdar)
• Notes on Modularity Lifting in the Ordinary Case (David Geraghty)
• p-Adic L-Functions for Hilbert Modular Forms (Mladen Dimitrov)
• Arithmetic of Adjoint L-Values (Haruzo Hida)
• p-Adic L-Functions for GLn (Debargha Banerjee and A Raghuram)
• Non-Triviality of Generalised Heegner Cycles Over Anticyclotomic Towers: A Survey (Ashay A Burungale)
• The Euler System of Heegner Points and p-Adic L-Functions (Ming-Lun Hsieh)
• Non-Commutative q-Expansions (Mahesh Kakde)

Readership: Researchers in algebra and number theory.
Key Features:

• Articles by some of the foremost experts in the field
• Includes down-to-earth exposition of the p-adic arithmetic theory to initiate learning by graduate students
• Contains cutting-edge material for professional researchers