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Toric periods and p-adic families of modular forms of half-integral weight
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 i...
Enregistré dans:
| Auteur principal : | |
|---|---|
| Format : | Livre |
| Langue : | anglais |
| Titre complet : | Toric periods and p-adic families of modular forms of half-integral weight / V. Vatsal |
| Publié : |
Providence (R.I.) :
American Mathematical Society
, 2023 |
| Description matérielle : | 1 volume (V-95 p.) |
| Collection : | Memoirs of the American Mathematical Society ; 1438 |
| Sujets : | |
| Documents associés : | Autre format:
Toric periods and p-adic families of modular forms of half-integral weight |
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| 200 | 1 | |a Toric periods and p-adic families of modular forms of half-integral weight |f V. Vatsal | |
| 214 | 0 | |a Providence (R.I.) |c American Mathematical Society |d 2023 | |
| 215 | |a 1 volume (V-95 p.) |d 26 cm | ||
| 225 | 0 | |a Memoirs of the American Mathematical Society |v number 1438 | |
| 320 | |a Bibliographie p.93-95 | ||
| 330 | |a 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 |2 abstract | ||
| 359 | 2 | |b Part 1: Global periods: Fourier coefficients of half-integer weight forms |b Part 2: Interpolation of the Fourier coefficients |b Part 3: Local periods: test vectors | |
| 410 | | | |0 013293931 |t Memoirs of the American Mathematical Society |x 0065-9266 |v 1438 | |
| 452 | | | |t Toric periods and p-adic families of modular forms of half-integral weight |y 978-1-4704-7593-2 | |
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