Research

Research Interests: My research interest is in the field of number theory, more specifically, I am interested in understanding the distributions of primes, smooth numbers, integers with digital restrictions, character sums, and other arithmetic functions using analytic and sieve theoretic techniques. I am also interested in exploring probabilistic techniques to solve problems in number theory.

Research Articles:

1. Poisson behavior for chains of small quadratic non-residues (with D. Basak and A. Zaharescu).

Int. Math. Res. Not. IMRN 2024, no. 4, 3356-3390. DOI: 10.1093/imrn/rnad168, [pdf][journal][slides]

2. Gaussian phenomena for small quadratic residues and non-residues (with D. Basak and A. Zaharescu).

Trans. Amer. Math. Soc. 376 (2023), no. 5, 3695-3724. DOI: 10.1090/tran/8853, [pdf][journal][slides]

3. Primes with a missing digit: Distribution in arithmetic progressions and an application in sieve theory.

J. Lond. Math. Soc. (2) 109 (2024), no. 1. DOI: 10.1112/jlms.12837, [pdf][arXiv][journal][slides]

4. Small gaps between primes and semi-linear sieve.

 Unpublished note (preprint available upon request).

Ph.D. Thesis: 

Primes with a missing digit: distribution in arithmetic progressions and sieve-theoretic applications. Thesis (Ph.D.), Université de Montréal, 2021. 

DOI: 1866/26278, [pdf][link] (The main results can be found in article 3 above).

Undergraduate Reading Projects:

1. Theta Functions, Eisenstein Series and Ramanujan's Congruences for Partition Functions (under Prof. Nayandeep Deka Baruah at Tezpur University, Assam, India), May-June, 2015. [pdf]

2. Dirichlet's theorem on primes in arithmetic progressions (under Dr. Soumya Das at the Indian Institute of Science, Bengaluru, India), May-July, 2013. [pdf]