Greetings! Welcome to the homepage about my mathematical activities.

I work primarily at the interface of number theory, combinatorics and algebra. My research investigates instances of successes and failures of certain local-global principles in number theory. This also involves using p-adic methods to address a wide class of number-theoretic problems.

My most recent submitted work is about superpolynomially large support in every irreducible factor of sparse polynomials. In this work, we prove existence of infinitely many polynomials with exactly \(m\) non-zero coefficients – each irreducible factor of which has at least superpolynomially many (in \(m\)) nonzero coefficients. This general interest result places polynomial factorization in a radically different category as compared to other algebraic operations such as composition, taking powers of polynomials etc. for which reverse-sparsity principles were established by Schinzel, by Erdős, by Fuchs, Zannier and several others. This same result also concerns a weaker constant \(K(m)\) defined by Schinzel who showed with Choudhry that \(K(m) > \text{max} \big\{2m, 0.014m^{1.22} \}\) using a result of Verdenius. Our result implies that \(K(m)\) is eventually larger than any polynomial in \(m\).

I also recently submitted another work on a rigidity principle regarding local-global principle for \(n^{th}\) powers. The main result of this article, colloquially speaking, is that whenever the local-global principle for \(n^{th}\) powers fails, it does not fail too badly. The result is quantitative, sharp and is accompanied by a dichotomy result that all subsets of rationals must satisfy.

My next work that is in preparation concerns the Dynamical Mordell-Lang Conjecture for split endomorphisms of \(\big(\mathbb{P}^{1}\big)^{g}\). Please keep in touch with this webpage for more soon.

My MR author ID is 1438156. My ORCID and zbMATH author ID can be accessed respectively by clicking here and here. The best way to reach me is through email at : (myfirstname)(mylastname)2024@gmail.com