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pro vyhledávání: '"Kohnen, Winfried"'
We generalize the linear relation formula between the square of normalized Hecke eigenforms of weight $k$ and normalized Hecke eigenforms of weight $2k$, to Rankin-Cohen brackets of general degree. As an ingredient of the proof, we also generalize a
Externí odkaz:
http://arxiv.org/abs/2405.16745
A generalized Riemann hypothesis states that all zeros of the completed Hecke $L$-function $L^*(f,s)$ of a normalized Hecke eigenform $f$ on the full modular group should lie on the vertical line $Re(s)=\frac{k}{2}.$ It was shown by Kohnen that there
Externí odkaz:
http://arxiv.org/abs/2002.00096
In this paper, we obtain formulas for the number of representations of positive integers as sums of arbitrarily many squares (and other polygonal numbers) with a certain natural weighting. The resulting weighted sums give Fourier coefficients of weig
Externí odkaz:
http://arxiv.org/abs/1904.06794
We determine a formula for the average values of L-series associated to eigenforms at complex values.
Comment: 13 pages, amslatex. Revised version following referee report
Comment: 13 pages, amslatex. Revised version following referee report
Externí odkaz:
http://arxiv.org/abs/1904.04219
Let $F$ and $G$ be Siegel cusp forms for $\Sp_4(\Z)$ and weights $k_1, k_2$ respectively. Also let $F$ and $G$ be Hecke eigenforms lying in distinct eigen spaces. Further suppose that neither $F$ nor $G$ is a Saito-Kurokawa lift. In this article, we
Externí odkaz:
http://arxiv.org/abs/1901.10965
Autor:
Choie, YoungJu, Kohnen, Winfried
We investigate non-vanishing properties of $L(f,s)$ on the real line, when $f$ is a Hecke eigenform of half-integral weight $k+{1\over 2}$ on $\Gamma_0(4).$
Externí odkaz:
http://arxiv.org/abs/1712.05660
Autor:
Hofmann, Eric, Kohnen, Winfried
The purpose of this paper is to study products of Fourier coefficients of an elliptic cusp form, $a(n)a(n + r)$ $(n \geq 1)$ for a fixed positive integer $r$, concerning both non-vanishing and non-negativity.
Comment: Minor revision: Several typ
Comment: Minor revision: Several typ
Externí odkaz:
http://arxiv.org/abs/1509.02431
Publikováno v:
In Journal of Number Theory June 2020 211:28-42
Akademický článek
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We give an explicit upper bound for the first sign change of the Fourier coefficients of an arbitrary non-zero Siegel cusp form $F$ of even integral weight on the Siegel modular group of arbitrary genus $ g\geq 2 $.
Externí odkaz:
http://arxiv.org/abs/1403.4712