Toric Periods and p-adic Families of Modular Forms of Half-Integral Weight / V. Vatsal.

Format:

Book

Author/Creator:

Vatsal, Vinayak, 1969- author.

Series:

Memoirs of the American Mathematical Society ; Volume 289.

Memoirs of the American Mathematical Society Series ; Volume 289

Language:

English

Subjects (All):

Algebra.

Number theory.

Physical Description:

1 online resource (108 pages)

Edition:

First edition.

Place of Publication:

Providence, RI : American Mathematical Society, [2023]

Summary:

The primary goal of this work is to construct $p$-adic families of modular forms of half-integral weight, by using Waldspurger's automorphic framework to make the results as comprehensive and precise as possible. A secondary goal is to clarify the role of test vectors as defined by Gross-Prasad in the elucidation of general formulae for the Fourier coefficients of modular forms of half-integral weight in terms of toric periods of the corresponding modular forms of integral weight. As a consequence of our work, we develop a generalization of a classical formula due to Shintani, and make precise the conditions under which Shintani's lift vanishes. We also give a number of results on test vectors for ramified representations which are of independent interest.

Contents:

Cover

Title page

Introduction

Part 1. Part 1: Global periods: Fourier coefficients of half-integer weight forms

Chapter 1. Preliminaries

Chapter 2. Classical and automorphic forms of half-integer weight

Chapter 3. Fourier coefficients of modular forms of half-integer weight

Part 2. Part 2: Interpolation of the Fourier coefficients

Chapter 4. Preliminaries and the basic formula

Chapter 5. ̃Λ-adic Waldspurger packets, and non-vanishing of the ̃Λ-adic lift.

Chapter 6. Specialization to trivial character, and the trivial zero

Part 3. Part 3: Local periods: test vectors

Chapter 7. Preliminaries and statement of results

Chapter 8. -types and the principal series

Chapter 9. The depth zero supercuspidal representations of ₂(\qq_{ }).

Bibliography

Back Cover.

Notes:

Includes bibliographical references.

Description based on print version record.

Other Format:

Print version: Vatsal, V. Toric Periods and p-adic Families of Modular Forms of Half-Integral Weight

ISBN:

1-4704-7593-6