Jyoti Sengupta

Nonvanishing of symmetric square -functions of cusp forms inside the critical strip

We shall give a certain nonvanishing result for the symmetric square L-function of an elliptic cuspidal Hecke eigenform w.r.t. the full modular group inside the critical strip.

Signs of Fourier coefficients of two cusp forms of different weights

We investigate sign changes of Fourier coefficients of cusp forms of different weights.

Beurling's Theorem and Characterization of Heat Kernel for Riemannian Symmetric Spaces of Noncompact Type

We prove Beurlings theorem for rank 1 Riemmanian symmetric spaces and relate it to the characterization of the heat kernel of the symmetric space.

SIGN CHANGES IN SHORT INTERVALS OF COEFFICIENTS OF SPINOR ZETA FUNCTION OF A SIEGEL CUSP FORM OF GENUS 2

In this paper, we establish a Voronoi formula for the spinor zeta function of a Siegel cusp form of genus 2. We deduce from this formula quantitative results on the number of its positive (respectively, negative) coefficients in some short intervals.

Projection of orbits and K multiplicities

Abstract In this article we give an explicit formula for the push forward of the Liouville measure of regular coadjoint orbits of connected, noncompact, semisimple Lie groups under the moment map arising from the Hamiltonian action of a maximal compact subgroup. We also discuss its connection with Frobenius reciprocity.

Beurling’s theorem for Riemannian symmetric spaces II

We prove two versions of Beurlings theorem for Riemannian symmetric spaces of arbitrary rank. One of them uses the group Fourier transform and the other uses the Helgason Fourier transform. This is the master theorem in the quantitative uncertainty principle.

Waldspurger’s Formula and Central Critical Values of L -Functions of Newforms in Weight Aspect

We shall give a proof of the Lindelof hypothesis in weight aspect on the average for central critical values of quadratic character twists of Hecke L-functions attached to cuspidal Hecke eigenforms. One of the basic tools will be Waldspurger’s results on central critical values of L-functions in weight aspect.

Bounds for Fourier-Jacobi Coefficients of Siegel Cusp Forms of Degree Two

We discuss and prove several estimates involving Peterrson norms of Fourier-Jacobi coefficients of Siegel cusp forms of degree two.