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Maass cusp forms for large eigenvalues [PDF]
Mathematics of Computation, 2003 We investigate the numerical computation of Maass cusp forms for the modular group corresponding to large eigenvalues. We present Fourier coefficients of two cusp forms whose eigenvalues exceed r=40000.
Then, H.
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Goldbach partitions and norms of cusp forms
Journal of Numerical Analysis and Approximation Theory, 2019 An integral formula for the Goldbach partitions requires uniform convergence of a complex exponential sum. The dependence of the coefficients of the series is found to be bounded by that of cusp forms.
Simon Brian Davis
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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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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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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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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 cusp forms of mixed type
Lietuvos Matematikos Rinkinys, 2003 The base of the space of cusp forms of type (−10, 17, χ) is constructed in the form of the generalized quaternary theta series.
Edmundas Gaigalas
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