Research

My research interest is Number Theory and Automorphic forms, particularly Maass forms. The interplay between the classical and the representation theory side is of particular interest to me.

My current research is results related to the doubling methods. One of the projects I was working on was the stability of local gamma factors for GSpin groups, under the guidance of Prof. Eyal Kaplan. Another ongoing project is on the Borcherds lift to modular forms on 5-dimensonal hyperbolic space with Prof. Ameya Pitale . It is a generalization of the lift presented in following paper, which provides counterexamples to the generalized Ramanujan conjecture for an inner form of GL(4). I wish to further study the lift to obtain a relation between the Sup norm and the L2 norm.

In my thesis over the same paper, I gave a characterization of the image of the lift in terms of recurrence relations between Fourier coefficients. The previous methods of Maass, Kohnen or Kojima do not apply here, hence I approached this problem via a combination of classical and representation theory techniques to identify the image. Crucially, I used the Jacquet Langlands correspondence described by Badulescu and Renard to characterize the representations.

Publications:

1. ‘Stability of local gamma factors arising from the doubling method for general spin groups’ - https://arxiv.org/pdf/2104.12263.pdf.

2. ‘An explicit lifting construction of CAP forms on O(1, 5) ' - https://arxiv.org/pdf/2203.04853.pdf

3. ‘Maass space for lifting to GL(2,B) for a division quaternion algebra’ – Journal of Number Theory: In Press, Corrected Proof, https://doi.org/10.1016/j.jnt.2019.07.027 .

4. ‘Maass space for lifting from SL(2,R) to GL(2,B) over a division quaternion algebra’ – Contemporary Mathematics, Volume: 732; 2019; 286 pp; Softcover, MSC: Primary 11; 14; 22; 32; Page 257.

My Thesis titled ‘Maass space for lifting to GL(2,B) for a division quaternion algebra’ can be found here.