Aishik Chattopadhyay

collaborators

5 papers

math.NT2026

Burgess-Type volume centric Bounds for Character Sums over $F_{p^{n}}$

Aishik Chattopadhyay

We establish a Burgess-type bound for short multiplicative character sums over finite fields $F_{p^{n}}$ . Define box $B$ by $$ B=\left\{ \sum_{i=1}^{n} x_iÏ_i : N_i+1 \leq…

math.NT2026

Character sums to prime power moduli evaluated at binary quadratic forms

Stephan Baier, Aishik Chattopadhyay

We establish estimates for short character sums to prime power moduli evaluated at binary quadratic forms. This complements estimates established by Heath-Brown for such character…

math.NT2026

Small solutions of ternary quadratic congruences with averaging over the moduli

Stephan Baier, Aishik Chattopadhyay

In a recent paper, we proved that for any large enough odd modulus $q \in N$ and fixed $I^\pm_{2} \in N$ coprime to $q$ , the congruence \[ x_1^2+Î±_2x_2^2+Î±_3x_3^2\equi…

math.NT2025

Character sums over co-dimension one sub-lattices in finite field extensions

Aishik Chattopadhyay

We obtain nontrivial bounds for multiplicative character sums over codimension-one sublattices of finite field extensions $F_{p^{d}}$ . This extends earlier results of Davenp…

math.NT2025

Small Solutions of generic ternary quadratic congruences

Stephan Baier, Aishik Chattopadhyay

We consider small solutions of quadratic congruences of the form $x_{1}^{2} + I^\pm_{2} x_{2}^{2} + I^\pm_{3} x_{3}^{2} \equiv 0 mod q$ , where $q = p^{m}$ is an odd prime power. Here, $I^\pm_{2}$ is arbitrary but fi…

Burgess-Type volume centric Bounds for Character Sums over Fpn​

Character sums to prime power moduli evaluated at binary quadratic forms

Small solutions of ternary quadratic congruences with averaging over the moduli

Character sums over co-dimension one sub-lattices in finite field extensions

Small Solutions of generic ternary quadratic congruences

Burgess-Type volume centric Bounds for Character Sums over $F_{p^{n}}$