On metaplectic forms over function fields
Identifieur interne : 000157 ( Main/Exploration ); précédent : 000156; suivant : 000158On metaplectic forms over function fields
Auteurs : Fu-Tsun Wei [Taïwan]Source :
- Mathematische Annalen [ 0025-5831 ] ; 2013-01-01.
Abstract
Abstract: We propose a concept of half integral weight in the global function field context, and construct natural families of functions with given weight. An analogue of Shimura correspondence (between weight 2 functions and weight $${\frac{3}{2}}$$ functions) via theta series from “definite” quaternion algebras over function fields is then established. From the study of Fourier coefficients of these theta series, we arrive at a Waldspurger-type formula. This formula is then applied to L-series coming from elliptic curves over function fields.
Url:
DOI: 10.1007/s00208-012-0785-1
Affiliations:
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<front><div type="abstract" xml:lang="en">Abstract: We propose a concept of half integral weight in the global function field context, and construct natural families of functions with given weight. An analogue of Shimura correspondence (between weight 2 functions and weight $${\frac{3}{2}}$$ functions) via theta series from “definite” quaternion algebras over function fields is then established. From the study of Fourier coefficients of these theta series, we arrive at a Waldspurger-type formula. This formula is then applied to L-series coming from elliptic curves over function fields.</div>
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