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Hecke Operators and the . . .
, 1995
"... We determine some conditions which imply the nonvanishing of L f (k=2) for f a cusp form of weight k 0 mod 4 for the full modular group. These conditions are veried for weights k 500. ..."
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We determine some conditions which imply the nonvanishing of L f (k=2) for f a cusp form of weight k 0 mod 4 for the full modular group. These conditions are veried for weights k 500.
HECKE OPERATORS ON COHOMOLOGY
"... Abstract. Hecke operators play an important role in the theory of automorphic forms, and automorphic forms are closely linked to various cohomology groups. This paper is mostly a survey of Hecke operators acting on certain types of cohomology groups. The class of cohomology on which Hecke operator ..."
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Abstract. Hecke operators play an important role in the theory of automorphic forms, and automorphic forms are closely linked to various cohomology groups. This paper is mostly a survey of Hecke operators acting on certain types of cohomology groups. The class of cohomology on which Hecke
Modular symbols and Hecke operators
, 2000
"... Abstract. We survey techniques to compute the action of the Hecke operators on the cohomology of arithmetic groups. These techniques can be seen as generalizations in different directions of the classical modular symbol algorithm, due to Manin and AshRudolph. Most of the ..."
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Abstract. We survey techniques to compute the action of the Hecke operators on the cohomology of arithmetic groups. These techniques can be seen as generalizations in different directions of the classical modular symbol algorithm, due to Manin and AshRudolph. Most of the
Hecke operators for GLn and buildings
 Acta Arith
"... We describe a representation of the local Hecke algebra for GLn in which the Hecke operators act on the vertices of the BruhatTits building for SLn(Qp). We also give a geometric interpretation of this representation, characterizing the action of our operators on a vertex in terms of the endpoints o ..."
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We describe a representation of the local Hecke algebra for GLn in which the Hecke operators act on the vertices of the BruhatTits building for SLn(Qp). We also give a geometric interpretation of this representation, characterizing the action of our operators on a vertex in terms of the endpoints
Harmonic Analysis and Hecke Operators
 in Rigidity in Dynamics and Geometry
, 2002
"... Abstract. We first construct new uniform pointwise bounds for the matrix coefficients of infinite dimensional unitary representations of a reductive algebraic group over a local field k with semisimple krank at least 2 [21]. We explain how this information on local harmonic analysis yields norm es ..."
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estimates for (global) Hecke operators on L2(Γ\G) for a connected almost simple simply connected Qgroup G and its congruence subgroup Γ [5]. With the tool of Hecke operators, we settle a question of Linnik raised in the early sixties on the distribution of integer points of Diophantine type varieties when
THE PARTITION FUNCTION AND HECKE OPERATORS
"... Abstract. The theory of congruences for the partition function p(n) depends heavily on the properties of halfintegral weight Hecke operators. The subject has been complicated by the absence of closed formulas for the Hecke images P (z)  T (ℓ2), where P (z) is the relevant modular generating funct ..."
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Cited by 2 (0 self)
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Abstract. The theory of congruences for the partition function p(n) depends heavily on the properties of halfintegral weight Hecke operators. The subject has been complicated by the absence of closed formulas for the Hecke images P (z)  T (ℓ2), where P (z) is the relevant modular generating
Rationality theorems for Hecke operators on GLn
 J. Number Theory
"... We define n families of Hecke operators T n k (pℓ) for GLn whose generating series ..."
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Cited by 6 (3 self)
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We define n families of Hecke operators T n k (pℓ) for GLn whose generating series
Hecke operators on de Rham cohomology
"... We introduce Hecke operators on de Rham cohomology of compact oriented manifolds. When the manifold is a quotient of a Hermitian symmetric domain, we prove that certain types of such operators are compatible with the usual Hecke operators on automorphic forms. ..."
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We introduce Hecke operators on de Rham cohomology of compact oriented manifolds. When the manifold is a quotient of a Hermitian symmetric domain, we prove that certain types of such operators are compatible with the usual Hecke operators on automorphic forms.
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