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Discrepancy results for modular forms

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dc.contributor.advisor BALASUBRAMANYAM, BASKAR
dc.contributor.advisor SINHA, KANEENIKA
dc.contributor.author DAS, JISHU
dc.date.accessioned 2023-12-20T03:50:03Z
dc.date.available 2023-12-20T03:50:03Z
dc.date.issued 2023-11
dc.identifier.citation 84 en_US
dc.identifier.uri http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/8365
dc.description.abstract Let F be a totally real number field, r = [F : Q], and N be an integral ideal. Let Ak(N, ω) be the space of holomorphic Hilbert cusp forms with respect to K1(N), weight k = (k1, ..., kr) with kj > 2, kj even for all j and central Hecke character ω. For a fixed level N, we study the behavior of the Petersson trace formula for the Hecke operators acting on Ak(N, ω) as k0 → ∞ where k0 = min(k1, ..., kr) subjected to a given condition. We give an asymptotic formula for the Petersson formula under certain conditions. As an application, we generalize a discrepancy result for classical cusp forms with squarefree levels by Jung and Sardari to Hilbert cusp forms for F with the ring of integers O having class number 1, odd narrow class number, and the ideals being generated by numbers belonging to Z. In the second part, we restrict ourselves to classical cusp forms i.e. when the field is Q. We obtain a generalization for the discrepancy result in the context of levels (of the form 2a × b with b odd, a = 0, 1, 2) and the space of old forms. Then we get a similar kind of lower bound for λp2 (f) for an eigenform f. en_US
dc.description.sponsorship CSIR en_US
dc.language.iso en en_US
dc.subject Modular forms en_US
dc.subject trace formula en_US
dc.subject Research Subject Categories::MATHEMATICS en_US
dc.subject Number Theory en_US
dc.subject Discrepancy en_US
dc.title Discrepancy results for modular forms en_US
dc.type Thesis en_US
dc.description.embargo No Embargo en_US
dc.type.degree Ph.D en_US
dc.contributor.department Dept. of Mathematics en_US
dc.contributor.registration 20183617 en_US


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  • PhD THESES [590]
    Thesis submitted to IISER Pune in partial fulfilment of the requirements for the degree of Doctor of Philosophy

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