p-Adic Aspects of Modular Forms

Nonfiction, Science & Nature, Mathematics, Research, Number Theory
Cover of the book p-Adic Aspects of Modular Forms by Baskar Balasubramanyam, Haruzo Hida, A Raghuram;Jacques Tilouine, World Scientific Publishing Company
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Author: Baskar Balasubramanyam, Haruzo Hida, A Raghuram;Jacques Tilouine ISBN: 9789814719247
Publisher: World Scientific Publishing Company Publication: June 14, 2016
Imprint: WSPC Language: English
Author: Baskar Balasubramanyam, Haruzo Hida, A Raghuram;Jacques Tilouine
ISBN: 9789814719247
Publisher: World Scientific Publishing Company
Publication: June 14, 2016
Imprint: WSPC
Language: English

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
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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:

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

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