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Modular forms with non-vanishing central values and linear independence of Fourier coefficients

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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


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