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 ; no. 1438.

Memoirs of the American Mathematical Society, 0065-9266 ; no. 1438

Language:

English

Subjects (All):

Forms, Modular.

Number theory.

Algebra.

algebra.

Physical Description:

v, 95 pages ; 26 cm.

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 to test vectors for ramified representations which are of independent interest.

Contents:

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

Part 2: Interpolation of the Fourier coefficients

Part 3: Local periods: test vectors.

Notes:

Includes bibliographical references (pages 93-95).

ISBN:

9781470465506

1470465507

OCLC:

1402286936