We show that the Hecke algebra module carried by the involutions in a Weyl group (defined by the author and Vogan) can be identified with a left ideal in the Hecke algebra. An analogous result is proved for any Coxeter group.

We derive a parameterization of simple modules for the cyclotomic Hecke algebras of type G(r, p, n) over field of any (coprime to p) characteristic. We give explicit formulas for the number of simple modules over these cyclotomic Hecke algebras.

2 Modular forms and Automorphic forms 2 2.1 Modular Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 The Adele group of GL2 over Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Automorphic Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Hecke act...

Hecke Schrobsdorff, Matthias Ihrke, Björn Kabisch Jörg Behrendt, Marcus Hasselhorn, J. Michael Herrmann 1 Bernstein Center for Computational Neuroscience Göttingen 2 Institute for Nonlinear Dynamics, Göttingen University Bunsenstr. 10, 37073 Göttingen, Germany 3 Georg-Elias-Müller-Institute, Göttingen University Waldweg 26, 37073 Göttingen, Germany hecke|[email protected], bjoern.kabisch@gm...

We sharpen some estimates of Rankin on power sums of Hecke eigenvalues, by using Kim & Shahidi’s recent results on higher order symmetric powers. As an application, we improve Kohnen, Lau & Shparlinski’s lower bound for the number of Hecke eigenvalues of same signs.

In this paper an explicit formula is given for a sequence of numbers. The positivity of this sequence of numbers implies that zeros in the critical strip of the Euler product of Hecke polynomials, which are associated with the space of cusp forms of weight k for Hecke congruence subgroups, lie on the critical line.

We compute the Selberg trace formula for Hecke operators (also called the trace formula for modular correspondences) in the context of cocompact Kleinian groups with finite-dimentional unitary representations. We give some applications to the distribution of Hecke eigenvalues, and give an analogue of Huber’s theorem.

Let K be a number field of degree n. We show that the maximal parabolic Eisenstein series on GL(n), restricted to the non-split torus obtained from K, has a Fourier expansion, and that the Fourier coefficients may be expressed in terms of Hecke L-functions. This is an analogue of the computation of the classical hyperbolic expansion of the GL(2) nonholomorphic Eisenstein series. We also show th...

These notes are an expanded version of the Aisenstadt lectures given at the CRM, Université de Montréal, in May/June 2002; they also include material from lectures given at MIT during the Fall of 1999 [L12]. I wish to thank Jacques Hurtubise for inviting me to give the Aisenstadt lectures. Hecke algebras arise as endomorphism algebras of representations of groups induced by representations of s...

In this paper we give a proof of the Hecke quantum unique ergodic-ity rate conjecture for the Berry-Hannay model. A model of quantum mechanics on the 2-dimensional torus. In the paper " Quantization of linear maps on the torus-Fresnel diffrac-tion by a periodic grating " , published in 1980 (see [BH]), the physicists M.V. Berry and J. Hannay explore a model for quantum mechanics on the 2-dimens...