dc.contributor.author |
BANERJEE, DEBARGHA |
en_US |
dc.contributor.author |
Majumder, Priyanka |
en_US |
dc.date.accessioned |
2024-08-28T05:17:56Z |
|
dc.date.available |
2024-08-28T05:17:56Z |
|
dc.date.issued |
2024-08 |
en_US |
dc.identifier.citation |
Ramanujan Journal |
en_US |
dc.identifier.issn |
1382-4090 |
en_US |
dc.identifier.issn |
1572-9303 |
en_US |
dc.identifier.uri |
https://doi.org/10.1007/s11139-024-00931-5 |
en_US |
dc.identifier.uri |
http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/9057 |
|
dc.description.abstract |
In this article, we are interested in modular forms with non-vanishing central critical values and linear independence of Fourier coefficients of modular forms. The main ingredient is a generalization of a theorem due to VanderKam to modular symbols of higher weights. We prove that for sufficiently large primes p, Hecke operators T-1,T-2,& mldr;,T-D act linearly independently on the winding elements inside the space of weight 2k cuspidal modular symbol S-2k(Gamma(0)(p)) with k >= 1 for D-2 << p. This gives a bound on the number of newforms with non-vanishing arithmetic L-functions at their central critical points and linear independence on the reductions of these modular forms for prime modulo l not equal p. |
en_US |
dc.language.iso |
en |
en_US |
dc.publisher |
Springer Nature |
en_US |
dc.subject |
Modular curves |
en_US |
dc.subject |
Hecke operators |
en_US |
dc.subject |
Central L-values |
en_US |
dc.subject |
Modular symbols |
en_US |
dc.subject |
2024-AUG-WEEK2 |
en_US |
dc.subject |
TOC-AUG-2024 |
en_US |
dc.title |
Modular forms with non-vanishing central values and linear independence of Fourier coefficients |
en_US |
dc.type |
Article |
en_US |
dc.contributor.department |
Dept. of Mathematics |
en_US |
dc.identifier.sourcetitle |
Ramanujan Journal |
en_US |
dc.publication.originofpublisher |
Foreign |
en_US |