Displaying similar documents to “An analytic function and iterated integrals”

Quantum unique ergodicity for Eisenstein series on P S L 2 ( P S L 2 ( )

Dmitry Jakobson (1994)

Annales de l'institut Fourier

Similarity:

In this paper we prove microlocal version of the equidistribution theorem for Wigner distributions associated to Eisenstein series on P S L 2 ( ) P S L 2 ( ) . This generalizes a recent result of W. Luo and P. Sarnak who proves equidistribution for P S L 2 ( ) . The averaged versions of these results have been proven by Zelditch for an arbitrary finite-volume surface, but our proof depends essentially on the presence of Hecke operators and works only for congruence subgroups of S L 2 ( ) . In the proof the key estimates come...

One special class of modular forms and group representations

Galina V. Voskresenskaya (1999)

Journal de théorie des nombres de Bordeaux

Similarity:

In this article we consider one special class of modular forms which are products of Dedekind η -functions and the relationships between these functions and representations of finite groups.

From pseudodifferential analysis to modular form theory

André Unterberger (1999)

Journées équations aux dérivées partielles

Similarity:

Taking advantage of methods originating with quantization theory, we try to get some better hold - if not an actual construction - of Maass (non-holomorphic) cusp-forms. We work backwards, from the rather simple results to the mostly devious road used to prove them.

On sums of three squares

James W. Cogdell (2003)

Journal de théorie des nombres de Bordeaux

Similarity:

We address the question of when an integer in a totally real number field can be written as the sum of three squared integers from the field and more generally whether it can be represented by a positive definite integral ternary quadratic form over the field. In recent work with Piatetski-Shapiro and Sarnak we have shown that every sufficiently large totally positive square free integer is globally integrally represented if and only if it is so locally at all places, thus essentially...

A spectral analysis of automorphic distributions and Poisson summation formulas

André Unterberger (2004)

Annales de l’institut Fourier

Similarity:

Automorphic distributions are distributions on d , invariant under the linear action of the group S L ( d , ) . Combs are characterized by the additional requirement of being measures supported in d : their decomposition into homogeneous components involves the family ( 𝔈 i λ d ) λ , of Eisenstein distributions, and the coefficients of the decomposition are given as Dirichlet series 𝒟 ( s ) . Functional equations of the usual (Hecke) kind relative to 𝒟 ( s ) turn out to be equivalent to the invariance of the comb under some modification...