Gram points in the theory of zeta-functions of certain cusp forms
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DOI: 10.1016/j.jmaa.2021.125396
Abstract: Abstract In the paper, an analogue of the Gram points used in the theory of the Riemann zeta-function is introduced for zeta-functions of normalized Hecke-eigen cusp forms of weight κ. Some analytic properties of those… read more here.
Keywords: points theory; functions certain; zeta functions; cusp forms ... See more keywords
Eichler–Shimura isomorphism in higher level cases and its applications
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DOI: 10.1016/j.jnt.2017.01.002
Abstract: Abstract Let Γ be a Fuchsian group of the first kind. The Eichler–Shimura isomorphism states that the space S k ( Γ ) is isomorphic to the first (parabolic) cohomology group associated to the Γ-module… read more here.
Keywords: cusp forms; isomorphism higher; shimura isomorphism; eichler shimura ... See more keywords
On newforms of half-integral weight and Jacobi forms
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DOI: 10.1016/j.jnt.2018.05.002
Abstract: Abstract Let N be an odd and square-free integer. Let α be a positive integer with α = 2 or α = 5 . Let χ modulo N be a Dirichlet character and let χ… read more here.
Keywords: cusp forms; newforms half; integral weight; jacobi ... See more keywords
Drinfeld cusp forms: oldforms and newforms
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DOI: 10.1016/j.jnt.2020.03.011
Abstract: Abstract Let p = ( P ) be any prime of F q [ t ] , let m be any ideal of F q [ t ] not divisible by p and consider the… read more here.
Keywords: cusp forms; drinfeld cusp; oldforms newforms; forms oldforms ... See more keywords
Bounds for the Bergman Kernel and the Sup-Norm of Holomorphic Siegel Cusp Forms
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DOI: 10.1093/imrn/rnad322
Abstract: We prove “polynomial in $k$” bounds on the size of the Bergman kernel for the space of holomorphic Siegel cusp forms of degree $n$ and weight $k$. When $n=1,2$ our bounds agree with the conjectural… read more here.
Keywords: holomorphic siegel; cusp forms; bergman kernel; siegel cusp ... See more keywords
Plancherel Distribution of Satake Parameters of Maass Cusp Forms on GL3
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DOI: 10.1093/imrn/rny061
Abstract: We prove an equidistribution result for the Satake parameters of Maass cusp forms on $GL_3$ with respect to the $p$-adic Plancherel measure by using an application of the Kuznetsov trace formula. The techniques developed in… read more here.
Keywords: satake parameters; cusp forms; parameters maass; maass cusp ... See more keywords
An asymptotic expansion of a Lambert series associated to cusp forms
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DOI: 10.1142/s1793042118500173
Abstract: Zagier’s conjecture on the asymptotic expansion of the Lambert series ∑n=1∞τ2(n)exp(−nz), where τ(n) is the Ramanujan’s tau function, was proved by Hafner and Stopple. Recently, Chakraborty, Kanemitsu and Maji have extended this result to any… read more here.
Keywords: cusp forms; asymptotic expansion; expansion lambert; lambert series ... See more keywords
On triple correlations of Fourier coefficients of cusp forms. II
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DOI: 10.1142/s1793042119500374
Abstract: The triple correlation [Formula: see text] for arbitrary coefficients [Formula: see text] is estimated on average over [Formula: see text] in some short intervals. By introducing a device of short intervals, we are able to… read more here.
Keywords: see text; formula see; cusp forms; short intervals ... See more keywords
A note on arithmetic behavior of Hecke eigenvalues of Siegel cusp forms of degree two
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DOI: 10.1142/s1793042122500026
Abstract: Let [Formula: see text] and [Formula: see text] be Siegel cusp forms for the group [Formula: see text] with weights [Formula: see text], [Formula: see text], respectively. Suppose that neither [Formula: see text] nor [Formula:… read more here.
Keywords: siegel cusp; formula see; cusp forms; see text ... See more keywords