Zobrazeno 1 - 10
of 59
pro vyhledávání: '"Marvin I. Knopp"'
Autor:
Bruce C Berndt, Marvin I Knopp
In 1938, at the Institute for Advanced Study, E Hecke gave a series of lectures on his theory of correspondence between modular forms and Dirichlet series. Since then, the Hecke correspondence has remained an active feature of number theory and, inde
Autor:
Mark Sheingorn, Marvin I. Knopp
Publikováno v:
The Ramanujan Journal. 41:31-50
We track the trajectories of individual directed horocycles on the modular surface. Our tracking is constructive, and we thus effectively establish topological transitivity and even line-transitivity for the horocyclic flow.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::bfe9130c42f29689804ee3228217c8d5
https://doi.org/10.1007/s11139-014-9607-2
https://doi.org/10.1007/s11139-014-9607-2
Autor:
Geoffrey Mason, Marvin I. Knopp
Publikováno v:
The Ramanujan Journal. 29:213-223
We establish (Theorem 3.6) polynomial-growth estimates for the Fourier coefficients of holomorphic logarithmic vector-valued modular forms.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::aab4d07155d91a7603dd2e2ab655aca2
https://doi.org/10.1007/s11139-011-9363-5
https://doi.org/10.1007/s11139-011-9363-5
Autor:
Marvin I. Knopp, Geoffrey Mason
Publikováno v:
International Journal of Number Theory. :859-864
The paper "Parabolic Generalized Modular Forms and Their Characters" which previously appeared in this journal, contained several anomalies in Sec. 3, "Structure of [Formula: see text]", arising from a mishandling of complex powers of the functions d
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f0f86fc7c12b53c20aa60dee6f9f4ea2
https://doi.org/10.1142/s1793042112500509
https://doi.org/10.1142/s1793042112500509
Autor:
Geoffrey Mason, Marvin I. Knopp
Publikováno v:
Acta Arithmetica. 147:261-282
We consider logarithmic vector- and matrix-valued modular forms of integral weight $k$ associated with a $p$-dimensional representation $\rho: SL_2(\mathbb{Z}) \to GL_p(\mathbb{C})$ of the modular group, subject only to the condition that $\rho(T)$ h
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2a3ddf799c40253ad175b9e3db0ae08f
https://doi.org/10.4064/aa147-3-6
https://doi.org/10.4064/aa147-3-6
Autor:
Henok Mawi, Marvin I. Knopp
Publikováno v:
Proceedings of the American Mathematical Society. 138:395-404
Let Γ be an H-group. In 1974 Marvin Knopp conjectured that the Eichler cohomology group, with base space taken to be the set of all functions holomorphic in the upper half-plane, of polynomial growth at the real line (including oo), and with a weigh
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::65b13830ad5424f9d76acf61e8d6d96d
https://doi.org/10.1090/s0002-9939-09-10070-9
https://doi.org/10.1090/s0002-9939-09-10070-9
Publikováno v:
International Journal of Number Theory. :1049-1059
By using Stokes's theorem, we prove an Eichler cohomology theorem for generalized modular forms with some restrictions on the relevant multiplier systems.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2738e7245f35507223efa89dadb0a670
https://doi.org/10.1142/s1793042109002547
https://doi.org/10.1142/s1793042109002547
Autor:
Geoffrey Mason, Marvin I. Knopp
Publikováno v:
International Journal of Number Theory. :845-857
We make a detailed study of the generalized modular forms of weight zero and their associated multiplier systems (characters) on an arbitrary subgroup Γ of finite index in the modular group. Among other things, we show that every generalized divisor
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::65128727dbf9a173a1d0414eed0e9c2f
https://doi.org/10.1142/s1793042109002419
https://doi.org/10.1142/s1793042109002419
Publikováno v:
The Ramanujan Journal. 12:327-347
We discuss equivalent definitions of holomorphic second-order cusp forms and prove bounds on their Fourier coefficients. We also introduce their associated L-functions, prove functional equations for twisted versions of these L-functions and establis
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5e8bd75e25e835a37eba16e0a07e3885
https://doi.org/10.1007/s11139-006-0147-2
https://doi.org/10.1007/s11139-006-0147-2
A memorial conference for Leon Ehrenpreis was held at Temple University, November 15-16, 2010. In the spirit of Ehrenpreis's contribution to mathematics, the papers in this volume, written by prominent mathematicians, represent the wide brea