scholarly journals p-adic Asai L-functions Attached to Bianchi Cusp Forms

2020 ◽  
pp. 19-45
Author(s):  
Baskar Balasubramanyam ◽  
Eknath Ghate ◽  
Ravitheja Vangala
Keyword(s):  
Cusp Forms

Congruences between Hilbert Cusp Forms

2018 ◽  
Author(s):  
Hiroshi Saito ◽  
Masatoshi Yamauchi
Keyword(s):  
Cusp Forms

scholarly journals On triple correlations of Fourier coefficients of cusp forms

2018 ◽  
Vol 183 ◽  
pp. 485-492 ◽  
Author(s):  
Guangshi Lü ◽  
Ping Xi
Keyword(s):  
Fourier Coefficients ◽  
Cusp Forms

scholarly journals CONSTRUCTING SIMULTANEOUS HECKE EIGENFORMS

2010 ◽  
Vol 06 (05) ◽  
pp. 1117-1137 ◽  
Author(s):  
T. SHEMANSKE ◽  
S. TRENEER ◽  
L. WALLING
Keyword(s):  
Hecke Operators ◽  
Cusp Forms ◽  
Hecke Eigenforms ◽  
Linearly Independent ◽  
Integral Weight ◽  
Trivial Character ◽  
Free Level ◽  
Fixed Space ◽  
Space Of Cusp Forms

It is well known that newforms of integral weight are simultaneous eigenforms for all the Hecke operators, and that the converse is not true. In this paper, we give a characterization of all simultaneous Hecke eigenforms associated to a given newform, and provide several applications. These include determining the number of linearly independent simultaneous eigenforms in a fixed space which correspond to a given newform, and characterizing several situations in which the full space of cusp forms is spanned by a basis consisting of such eigenforms. Part of our results can be seen as a generalization of results of Choie–Kohnen who considered diagonalization of "bad" Hecke operators on spaces with square-free level and trivial character. Of independent interest, but used herein, is a lower bound for the dimension of the space of newforms with arbitrary character.

scholarly journals A Selberg trace formula for hypercomplex analytic cusp forms

2015 ◽  
Vol 148 ◽  
pp. 398-428 ◽  
Author(s):  
D. Grob ◽  
R.S. Kraußhar
Keyword(s):  
Trace Formula ◽  
Cusp Forms ◽  
Selberg Trace Formula
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