Results 21 to 30 of about 8,678 (292)
Proceedings of the National Academy of Sciences, 1985 It is shown that, under certain standard assumptions, such as extended Riemann hypotheses, the scattering matrix ϕ( s ) for generic Γ ≤ SL(2, R) is unexpectedly of order 2. This leads to the conjecture that the generic cofinite Γ has very few Maass cusp forms.
Deshouillers, J.-M. +3 more
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On zeta-functions associated to certain cusp forms. II
Open Mathematics, 2009 A formula for the mean value of multiplicative functions associated to certain cusp forms is obtained. The paper is a continuation of [4]
Laurinčikas Antanas +2 more
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Superlacunary cusp forms [PDF]
Proceedings of the American Mathematical Society, 1995 A power series is called superlacunary if it has the form \[ f(x)= \sum_{n=-\infty}^\infty d(an^2+ bn+ c) x^{an^2+ bn +c} \] where \(a\), \(b\), \(c\) are integers with \(a>0\). The authors show there are no superlacunary integer weight cusp forms that are eigenforms of the Hecke operators \(T_p\).
Ono, Ken, Robins, Sinai
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On zeta-functions of cusp forms
Lietuvos Matematikos Rinkinys, 2004 There is not abstract.
Antanas Laurinčikas
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Explicit construction of mock modular forms from weakly holomorphic Hecke eigenforms
Open Mathematics, 2022 Extending our previous work we construct weakly holomorphic Hecke eigenforms whose period polynomials correspond to elements in a basis consisting of odd and even Hecke eigenpolynomials induced by only cusp forms.
Choi SoYoung, Kim Chang Heon
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Joint Universality of the Zeta-Functions of Cusp Forms
Mathematics, 2021 Let F be the normalized Hecke-eigen cusp form for the full modular group and ζ(s,F) be the corresponding zeta-function. In the paper, the joint universality theorem on the approximation of a collection of analytic functions by shifts (ζ(s+ih1τ,F),…,ζ(s ...
Renata Macaitienė
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On the lifting of Hilbert cusp forms to Hilbert-Siegel cusp forms [PDF]
Annales scientifiques de l'École normale supérieure, 2020 39 ...
Tamotsu, I., Yamana, S.
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Mathematics of Computation, 2014 We classify Siegel modular cusp forms of weight two for the paramodular group K(p) for primes p< 600. We find that weight two Hecke eigenforms beyond the Gritsenko lifts correspond to certain abelian varieties defined over the rationals of conductor p. The arithmetic classification is in a companion article by A. Brumer and K. Kramer.
Cris Poor, David S. Yuen
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Cusp forms as p-adic limits [PDF]
Journal of Number Theory, 2022 Ahlgren and Samart relate three cusp forms with complex multiplication to certain weakly holomorphic modular forms using $p$-adic bounds related to their Fourier coefficients. In these three examples, their result strengthens a theorem of Guerzhoy, Kent, and Ono which pairs certain CM forms with weakly holomorphic modular forms via $p$-adic limits ...
Michael Hanson, Marie Jameson
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