Explicit Hecke series for symplectic group of genus 4

Kirill Vankov

Displaying similar documents to “Explicit Hecke series for symplectic group of genus 4”

The universality theorem for Hecke L-functions

Hidehiko Mishou (2003)

Acta Arithmetica

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Hecke-Clifford algebras and spin Hecke algebras. IV: Odd double affine type.

Khongsap, Ta, Wang, Weiqiang (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Hecke operators on de Rham cohomology.

Min Ho Lee (2004)

Revista Matemática Complutense

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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.

On a conjecture of Watkins

Neil Dummigan (2006)

Journal de Théorie des Nombres de Bordeaux

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Watkins has conjectured that if $R$ is the rank of the group of rational points of an elliptic curve $E$ over the rationals, then $2^{R}$ divides the modular parametrisation degree. We show, for a certain class of $E$ , chosen to make things as easy as possible, that this divisibility would follow from the statement that a certain $2$ -adic deformation ring is isomorphic to a certain Hecke ring, and is a complete intersection. However, we show also that the method developed by Taylor, Wiles and others,...

The first negative Hecke eigenvalue of a Siegel cusp form of genus two

Winfried Kohnen, Jyoti Sengupta (2007)

Acta Arithmetica

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Products of an arbitrary number of Hecke eigenforms

Brad A. Emmons, Dominic Lanphier (2007)

Acta Arithmetica

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Double affine Hecke algebras of rank 1 and the $ℤ_{3}$ -symmetric Askey-Wilson relations.

Ito, Tatsuro, Terwilliger, Paul (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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On Dirichlet Series and Petersson Products for Siegel Modular Forms

Siegfried Böcherer, Francesco Ludovico Chiera (2008)

Annales de l’institut Fourier

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We prove that the Dirichlet series of Rankin–Selberg type associated with any pair of (not necessarily cuspidal) Siegel modular forms of degree $n$ and weight $k \geq n / 2$ has meromorphic continuation to $ℂ$ . Moreover, we show that the Petersson product of any pair of square–integrable modular forms of weight $k \geq n / 2$ may be expressed in terms of the residue at $s = k$ of the associated Dirichlet series.

New models for the action of Hecke operators in spaces of Maass wave forms

Ian Kiming (2007)

Annales de l’institut Fourier

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Utilizing the theory of the Poisson transform, we develop some new concrete models for the Hecke theory in a space $M_{λ} (N)$ of Maass forms with eigenvalue $1 / 4 - λ^{2}$ on a congruence subgroup $Γ_{1} (N)$ . We introduce the field $F_{λ} = ℚ (λ, \sqrt{n}, n^{λ / 2} ∣ n \in ℕ)$ so that $F_{λ}$ consists entirely of algebraic numbers if $λ = 0$ . The main result of the paper is the following. For a packet $Φ = (ν_{p} ∣ p ∤ N)$ of Hecke eigenvalues occurring in $M_{λ} (N)$ we then have that either every $ν_{p}$ is algebraic over $F_{λ}$ , or else $Φ$ will – for some $m \in ℕ$ – occur in the first cohomology of a certain...