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Displaying 661 – 680 of 2110

Gravity, strings, modular and quasimodular forms

P. Marios Petropoulos, Pierre Vanhove (2012)

Annales mathématiques Blaise Pascal

Modular and quasimodular forms have played an important role in gravity and string theory. Eisenstein series have appeared systematically in the determination of spectrums and partition functions, in the description of non-perturbative effects, in higher-order corrections of scalar-field spaces, ...The latter often appear as gravitational instantons i.e. as special solutions of Einstein’s equations. In the present lecture notes we present a class of such solutions in four dimensions, obtained by...

Group cohomology and the singularities of the Selberg zeta function associated to a Kleinian group.

Bunke, Ulrich, Olbrich, Martin (1999)

Annals of Mathematics. Second Series

Growth of Selmer groups of Hilbert modular forms over ring class fields

Jan Nekovář (2008)

Annales scientifiques de l'École Normale Supérieure

We prove non-trivial lower bounds for the growth of ranks of Selmer groups of Hilbert modular forms over ring class fields and over certain Kummer extensions, by establishing first a suitable parity result.

Grundlagen einer independenten Theorie der elliptischen Modulfunctionen und Theorie der Multiplicatorgleichungen erster Stufe.

Hurwitz (1881)

Mathematische Annalen

Harmonic analysis in weighted $L_{2}$ -spaces

Jens Franke (1998)

Annales scientifiques de l'École Normale Supérieure

Harmonic analysis on semisimple $p$ -adic Lie algebras.

Kottwitz, Robert E. (1998)

Documenta Mathematica

Harmonic Differentials and Closed Geodesics on a Riemann Surface.

Stephen S. Kudla, John J. Millson (1979)

Inventiones mathematicae

Harmonic weak Maass-modular grids in higher level cases

Bumkyu Cho, SoYoung Choi, Chang Heon Kim (2013)

Acta Arithmetica

We extend Guerzhoy's Maass-modular grids on the full modular group SL₂(ℤ) to congruence subgroups Γ₀(N) and Γ₀⁺(p).

Hasse invariant and group cohomology.

Edixhoven, Bas, Khare, Chandrashekhar (2003)

Documenta Mathematica

Hauteur des correspondances de Hecke

Pascal Autissier (2003)

Bulletin de la Société Mathématique de France

L’objectif de cet article est de mesurer la complexité arithmétique de la courbe modulaire $X_{0} (N)$ en fonction du niveau $N$ . Pour ce faire, on utilise un morphisme fini (de degré 1 sur son image) de $X_{0} (N)$ vers une variété fixe $X (1) \times X (1)$ et on calcule la hauteur au sens d’Arakelov de l’image $T_{N}$ de ce morphisme. La hauteur employée est directement reliée à la hauteur de Faltings des courbes elliptiques. On a besoin pour cela de considérer une théorie d’Arakelov pour les faisceaux inversibles hermitiens $L_{1}^{2}$ -singuliers (au...

Hecke eigenforms in the cohomology of congruence subgroups of $SL (3, ℤ)$ .

van Geemen, Bert, van der Kallen, Wilberd, Top, Jaap, Verberkmoes, Alain (1997)

Experimental Mathematics

Hecke Eigenforms of Degree Two: Dirichlet Series and Euler Products.

Erik A. Lippa (1976)

Mathematische Annalen

Hecke eigenvalues for real quadratic fields.

Okada, Kaoru (2002)

Experimental Mathematics

Hecke operators and Lambert series.

L. Alayne Parson, Kenneth H. Rosen (1981)

Mathematica Scandinavica

Hecke operators for GLₙ and buildings

Cristina M. Ballantine, John A. Rhodes, Thomas R. Shemanske (2004)

Acta Arithmetica

Hecke operators in half-integral weight

Soma Purkait (2014)

Journal de Théorie des Nombres de Bordeaux

In [6], Shimura introduced modular forms of half-integral weight, their Hecke algebras and their relation to integral weight modular forms via the Shimura correspondence. For modular forms of integral weight, Sturm’s bounds give generators of the Hecke algebra as a module. We also have well-known recursion formulae for the operators $T_{p^{ℓ}}$ with $p$ prime. It is the purpose of this paper to prove analogous results in the half-integral weight setting. We also give an explicit formula for how operators $T_{p^{ℓ}}$ ...

Hecke operators on de Rham cohomology.

Min Ho Lee (2004)

Revista Matemática Complutense

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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