6 papers
Burgess-Type volume centric Bounds for Character Sums over
Aishik Chattopadhyay
We establish a Burgess-type bound for short multiplicative character sums over finite fields . Define box by $$ B=\left\{ \sum_{i=1}^{n} x_iÏ_i : N_i+1 \leq…
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…
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 and fixed coprime to , the congruence \[ x_1^2+α_2x_2^2+α_3x_3^2\equi…
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 . This extends earlier results of Davenp…
Small Solutions of generic ternary quadratic congruences
Stephan Baier, Aishik Chattopadhyay
We consider small solutions of quadratic congruences of the form , where is an odd prime power. Here, is arbitrary but fi…
Small solutions of generic ternary quadratic congruences to general moduli
Stephan Baier, Aishik Chattopadhyay
We study small non-trivial solutions of quadratic congruences of the form , with being an odd natural number, in an average sense. T…