Toric periods and p-adic families of modular forms of half-integral weight
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Bibliographic Information
Toric periods and p-adic families of modular forms of half-integral weight
（Memoirs of the American Mathematical Society, no. 1438）
American Mathematical Society, c2023
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"September 2023, volume 289, number 1438 (fourth of 6 numbers)"
Includes bibliographical references (p. 93-95)
Description and Table of Contents
Description
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.
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