Displaying similar documents to “A spectral analysis of automorphic distributions and Poisson summation formulas”

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.

p -adic measures attached to Siegel modular forms

Siegfried Böcherer, Claus-Günther Schmidt (2000)

Annales de l'institut Fourier

Similarity:

We study the critical values of the complex standard- L -function attached to a holomorphic Siegel modular form and of the twists of the L -function by Dirichlet characters. Our main object is for a fixed rational prime number p to interpolate p -adically the essentially algebraic critical L -values as the Dirichlet character varies thus providing a systematic control of denominators of critical values by generalized Kummer congruences. In order to organize this information we prove the existence...

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

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 ( ℤ ) ∖ P S L 2 ( ℝ ) . This generalizes a recent result of W. Luo and P. Sarnak who proves equidistribution for P S L 2 ( ℤ ) ∖ ℍ . 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 ( ℝ ) . In the proof the key estimates come...