Toric Periods and $p$-adic Families of Modular Forms of Half-Integral Weight
Seiten
2023
American Mathematical Society (Verlag)
978-1-4704-6550-6 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-6550-6 (ISBN)
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. We develop a generalization of a classical formula due to Shintani and make precise conditions under which Shintani's lift vanishes.
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.
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.
| Erscheinungsdatum | 14.11.2023 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4704-6550-7 / 1470465507 |
| ISBN-13 | 978-1-4704-6550-6 / 9781470465506 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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