On optimality of mollifiers
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909852830269440 |
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| author | Čech, Martin Matomäki, Kaisa |
| author_facet | Čech, Martin Matomäki, Kaisa |
| contents | Mollifiers are used in a variety of contexts, for instance to study the non-vanishing of $L$-functions. In this paper, we study the general question of finding optimal mollifiers and provide criteria to identify them provided the corresponding mollified moments can be computed. As an application, we study the non-vanishing of central values of Dirichlet $L$-functions. In particular we show that the Michel-Vanderkam mollifier is optimal in a wide class of balanced two-piece mollifiers as well as provide a new proof that the Iwaniec-Sarnak mollifier is optimal in a wide class of one-piece mollifiers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12526 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On optimality of mollifiers Čech, Martin Matomäki, Kaisa Number Theory 11M20 Mollifiers are used in a variety of contexts, for instance to study the non-vanishing of $L$-functions. In this paper, we study the general question of finding optimal mollifiers and provide criteria to identify them provided the corresponding mollified moments can be computed. As an application, we study the non-vanishing of central values of Dirichlet $L$-functions. In particular we show that the Michel-Vanderkam mollifier is optimal in a wide class of balanced two-piece mollifiers as well as provide a new proof that the Iwaniec-Sarnak mollifier is optimal in a wide class of one-piece mollifiers. |
| title | On optimality of mollifiers |
| topic | Number Theory 11M20 |
| url | https://arxiv.org/abs/2501.12526 |