scholarly journals Modular Symbols and Hecke Operators

2000 ◽  
pp. 347-357 ◽  
Author(s):  
Paul E. Gunnells
Keyword(s):  
Hecke Operators ◽  
Modular Symbols

scholarly journals Universal Fourier expansions of Bianchi modular forms

2019 ◽  
Vol 16 (04) ◽  
pp. 731-746
Author(s):  
Tian An Wong
Keyword(s):  
Modular Forms ◽  
Hecke Operators ◽  
Quadratic Fields ◽  
Imaginary Quadratic Fields ◽  
Modular Symbols ◽  
Fourier Expansions

We generalize Merel’s work on universal Fourier expansions to Bianchi modular forms over Euclidean imaginary quadratic fields, under the assumption of the nondegeneracy of a pairing between Bianchi modular forms and Bianchi modular symbols. Among the key inputs is a computation of the action of Hecke operators on Manin symbols, building upon the Heilbronn–Merel matrices constructed by Mohamed.

scholarly journals Hecke Operations and the Adams E2-Term Based on Elliptic Cohomology

1999 ◽  
Vol 42 (2) ◽  
pp. 129-138 ◽  
Author(s):  
Andrew Baker
Keyword(s):  
Spectral Sequence ◽  
Adams Spectral Sequence ◽  
Hecke Operators ◽  
Elliptic Cohomology

AbstractHecke operators are used to investigate part of the E2-term of the Adams spectral sequence based on elliptic homology. The main result is a derivation of Ext1 which combines use of classical Hecke operators and p-adic Hecke operators due to Serre.

scholarly journals Hecke operators for Γ0(N)

1983 ◽  
Vol 83 (1) ◽  
pp. 39-64 ◽  
Author(s):  
Arnold Pizer
Keyword(s):  
Hecke Operators

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 On Dirichlet series attached to cusp forms and the Siegel-zero

1984 ◽  
Vol 25 (1) ◽  
pp. 107-119 ◽  
Author(s):  
F. Grupp
Keyword(s):  
Dirichlet Series ◽  
Cusp Form ◽  
Fourier Expansion ◽  
Dirichlet Character ◽  
Hecke Operators ◽  
Cusp Forms ◽  
Siegel Zero ◽  
Image Position

Let k be an even integer greater than or equal to 12 and f an nonzero cusp form of weight k on SL(2, Z). We assume, further, that f is an eigenfunction for all Hecke-Operators and has the Fourier expansionFor every Dirichlet character xmod Q we define

scholarly journals Λ-adic modular symbols over totally real fields

2011 ◽  
pp. 841-865 ◽  
Author(s):  
Baskar Balasubramanyam ◽  
Matteo Longo
Keyword(s):  
Modular Symbols ◽  
Totally Real ◽  
Totally Real Fields

scholarly journals Modular Symbols have a Normal Distribution

2004 ◽  
Vol 14 (5) ◽  
pp. 1013-1043 ◽  
Author(s):  
Y. N. Petridis ◽  
M. S. Risager
Keyword(s):  
Normal Distribution ◽  
Modular Symbols

scholarly journals The Eisenstein elements of modular symbols for level product of two distinct odd primes

2016 ◽  
Vol 281 (2) ◽  
pp. 257-285 ◽  
Author(s):  
Debargha Banerjee ◽  
Srilakshmi Krishnamoorthy
Keyword(s):  
Modular Symbols
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