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Bounding hyperbolic and spherical coefficients of Maass forms, with V. Blomer, F. Brumley and A. Kontorovich
Maass forms Fourier coeffcients geodesics periods equidistribution Sobolev norms wave front lemma
2015/8/25
We develop a new method to bound the hyperbolic and spherical Fourier coecients of Maass forms de ned with respect to arbitrary uniform lattices.
Analytical Evaluation Of An Infinite Integral Over Four Spherical Bessel Functions
Analytical Evaluation Infinite Integral Four Spherical Bessel Functions
2011/3/1
Infinite integrals over spherical Bessel functions have always been of interest due to their occurence in nuclear physics [1-10], particle physics [11] and astrophysics [12-13],to mention a few.
On the Excursion Sets of Spherical Gaussian Eigenfunctions
Gaussian Eigenfunctions Excursion Sets Empirical Measure High Energy Asymptotics
2010/12/10
The high frequency behaviour for random eigenfunctions of the spherical Laplacian has been recently the object of considerable interest, also because of strong motivations arising from Physics and Cos...
A Pieri formula for Macdonald's spherical functions and polynomials
symmetric functions Hall-Littlewood polynomials Macdonald poly-nomials Pieri formulas root systems
2010/12/10
We present explicit Pieri formulas for Macdonald’s spherical func-tions (or generalized Hall-Littlewood polynomials associated with root sys-tems) and their q-deformation the Macdonald polynomials. Fo...
Beurling-Hörmander Uncertainty Principle for the Spherical Mean Operator
Uncertainty principle Beurling-Hö rmander theorem Gelfand-Shilov theorem Cowling-Price theorem Fourier transform Spherical mean operator
2010/1/22
We establish the Beurling-Hörmander theorem for the Fourier transform connected with the spherical mean operator. Applying this result, we prove the Gelfand-Shilov and Cowling-Price type theorems...