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9781470465506 Academic Inspection Copy

Toric Periods and $p$-adic Families of Modular Forms of Half-Integral Weight

  • ISBN-13: 9781470465506
  • Publisher: AMERICAN MATHEMATICAL SOCIETY
    Imprint: AMERICAN MATHEMATICAL SOCIETY
  • By V. Vatsal
  • Price: AUD $219.00
  • Stock: 0 in stock
  • Availability: This book is temporarily out of stock, order will be despatched as soon as fresh stock is received.
  • Local release date: 29/12/2023
  • Format: Paperback (254.00mm X 178.00mm) 95 pages Weight: 0g
  • Categories: Algebra [PBF]Algebraic topology [PBPD]
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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.
V. Vatsal, University of British Columbia, Vancouver, British Columbia, Canada.
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