scholarly journals Correspondences in Arakelov geometry and applications to the case of Hecke operators on modular curves

2011 ◽  
Vol 136 (3-4) ◽  
pp. 501-543 ◽  
Author(s):  
Ricardo Menares
Keyword(s):  
Hecke Operators ◽  
Modular Curves ◽  
Arakelov Geometry

scholarly journals Hecke operators on line bundles over modular curves

2012 ◽  
Vol 132 (4) ◽  
pp. 714-734
Author(s):  
Abhishek Banerjee
Keyword(s):  
Hecke Operators ◽  
Line Bundles ◽  
Modular Curves ◽  
On Line

Action of Hecke operators on cohomology of modular curves of level two

2012 ◽  
Vol 273 (3-4) ◽  
pp. 1139-1159
Author(s):  
Naoki Imai ◽  
Takahiro Tsushima
Keyword(s):  
Hecke Operators ◽  
Modular Curves

scholarly journals p-adic Dynamics of Hecke Operators on Modular Curves

2021 ◽  
Vol 33 (2) ◽  
pp. 387-431
Author(s):  
Eyal Z. Goren ◽  
Payman L Kassaei
Keyword(s):  
Hecke Operators ◽  
Modular Curves

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 the genus of some modular curves of level N

1996 ◽  
Vol 54 (2) ◽  
pp. 291-297 ◽  
Author(s):  
Chang Heon Kim ◽  
Ja Kyung Koo
Keyword(s):  
Modular Curves

We estimate the genus of the modular curves X1(N).

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

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