Results 1 to 10 of about 1,071 (24)
Universality of zeta-functions of cusp forms and non-trivial zeros of the Riemann zeta-function
Mathematical Modelling and Analysis, 2021 It is known that zeta-functions ζ(s,F) of normalized Hecke-eigen cusp forms F are universal in the Voronin sense, i.e., their shifts ζ(s + iτ,F), τ ∈ R, approximate a wide class of analytic functions.
Aidas Balčiūnas +4 more
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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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Nonlinear Analysis, 2020 In the paper, joint discrete universality theorems on the simultaneous approximation of a collection of analytic functions by a collection of discrete shifts of zeta-functions attached to normalized Hecke-eigen cusp forms are obtained.
Antanas Laurinčikas +2 more
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A Mixed Joint Universality Theorem for Zeta-Functions. II
Mathematical Modelling and Analysis, 2014 In the paper, a joint universality theorem on the approximation of analytic functions for zeta-function of a normalized Hecke eigen cusp form and a collection of periodic Hurwitz zeta-functions with algebraically independent parameters is obtained.
Vaida Pocevičienė +1 more
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Extension of the discrete universality theorem for zeta-functions of certain cusp forms
Nonlinear Analysis, 2018 In the paper, an universality theorem on the approximation of analytic functions by generalized discrete shifts of zeta functions of Hecke-eigen cusp forms is obtained.
Antanas Laurinčikas +2 more
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On modular Galois representations modulo prime powers [PDF]
, 2012 We study modular Galois representations mod $p^m$. We show that there are three progressively weaker notions of modularity for a Galois representation mod $p^m$: we have named these `strongly', `weakly', and `dc-weakly' modular.
Chen, Imin, Kiming, Ian, Wiese, Gabor
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Regularized inner products and weakly holomorphic Hecke eigenforms [PDF]
, 2017 We show that the image of repeated differentiation on weak cusp forms is precisely the subspace which is orthogonal to the space of weakly holomorphic modular forms.
Bringmann, Kathrin, Kane, Ben
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Statistical properties of zeta functions' zeros [PDF]
, 2014 The paper reviews existing results about the statistical distribution of zeros for the three main types of zeta functions: number-theoretical, geometrical, and dynamical.
Kargin, Vladislav
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Ramanujan type congruences for the Klingen-Eisenstein series
, 2014 In the case of Siegel modular forms of degree $n$, we prove that, for almost all prime ideals $\frak{p}$ in any ring of algebraic integers, mod $\frak{p}^m$ cusp forms are congruent to true cusp forms of the same weight.
Kikuta, Toshiyuki, Takemori, Sho
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, 2017 In this article, the authors give a lower bound on the number of sign changes of Fourier coefficients of a non-zero degree two Siegel cusp form of even integral weight on a Hecke congruence subgroup.
Gun, S., Sengupta, J.
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