A formula for the action of Hecke operators on half-integral weight Siegel modular forms and applications
| Autor: | Lynne H. Walling |
|---|---|
| Rok vydání: | 2013 |
| Předmět: |
Hecke algebra
Pure mathematics Algebra and Number Theory Mathematics - Number Theory Series (mathematics) Mathematics::Number Theory Modular form Operator theory Cusp form Algebra 11F46 Primary 11F60 11F37 11F27 11F30 Secondary FOS: Mathematics Number Theory (math.NT) Fourier series Hecke operator Mathematics Siegel modular form |
| Zdroj: | Journal of Number Theory. 133:1608-1644 |
| ISSN: | 0022-314X |
| DOI: | 10.1016/j.jnt.2012.10.007 |
| Popis: | We introduce an alternate set of generators for the Hecke algebra, and give an explicit formula for the action of these operators on Fourier coefficients. Using this, we compute the eigenvalues of Hecke operators acting on average Siegel theta series with half-integral weight (provided the prime associated to the operators does not divide the level of the theta series), and show that some of the Hecke operators annihilate theta series. Next, we bound the eigenvalues of these operators in terms of bounds on Fourier coefficients. Then we show that the half-integral weight Kitaoka subspace is stable under all Hecke operators. Finally, we observe that an obvious isomorphism between Siegel modular forms of weight k+1/2 and “even” Jacobi modular forms of weight k+1 is Hecke-invariant (here the level and character are arbitrary). |
| Databáze: | OpenAIRE |
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