Report
The Shimura lift and congruences for modular forms with the eta multiplier
| العنوان: | The Shimura lift and congruences for modular forms with the eta multiplier |
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| المؤلفون: | Ahlgren, Scott, Andersen, Nickolas, Dicks, Robert |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory |
| الوصف: | The Shimura correspondence is a fundamental tool in the study of half-integral weight modular forms. In this paper, we prove a Shimura-type correspondence for spaces of half-integral weight cusp forms which transform with a power of the Dedekind eta multiplier twisted by a Dirichlet character. We prove that the lift of a cusp form of weight $\lambda+1/2$ and level $N$ has weight $2\lambda$ and level $6N$, and is new at the primes $2$ and $3$ with specified Atkin-Lehner eigenvalues. This precise information leads to arithmetic applications. For a wide family of spaces of half-integral weight modular forms we prove the existence of infinitely many primes $\ell$ which give rise to quadratic congruences modulo arbitrary powers of $\ell$. Comment: 44 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2307.07438 |
| رقم الانضمام: | edsarx.2307.07438 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |