arXiv subjects

Soumya Das

Publications and source records attributed to Soumya Das.

38 records · Page 3Linked to original sources

arXiv2010

Non-vanishing of Jacobi Poincaré series

We prove that under suitable conditions, the Jacobi Poincaré series of exponential type of integer weight and matrix index does not vanish identically. For classical Jacobi forms, we construct a basis consisting of the "first" few Poincaré series and also give conditions both dependent and independent of the weight, which ensures non-vanishing of classical Jacobi Poincaré series. Equality of certain Kloosterman-type sums is proved. Also, a result on the non-vanishing of Jacobi Poincaré series is obtained when an odd prime divides the index.

math.NT↗

arXiv2009

Some aspects of Hermitian Jacobi forms

We introduce a certain differential (heat) operator on the space of Hermitian Jacobi forms of degree 1, show it's commutation with certain Hecke operators and use it to construct a lift of elliptic cusp forms to Hermitian Jacobi cusp forms. We construct Hermitian Jacobi forms as the image of the tensor product of two copies of Jacobi forms and also from differentiation of the variables. We determine the number of Fourier coefficients that determine a Hermitian Jacobi form and use it to embed a certain subspace of Hermitian Jacobi forms into a direct sum of modular forms for the full modular group.

math.NT↗