Anup Haldar

activity

20222024

collaborators

6 papers

math.NT2024

Small solutions to inhomogeneous and homogeneous quadratic congruences modulo prime powers

Stephan Baier, Arkaprava Bhandari, Anup Haldar

We prove asymptotic formulae for small weighted solutions of quadratic congruences of the form $λ_{1} x_{1}^{2} + \dots + λ_{n} x_{n}^{2} \equiv λ_{n + 1} mod p^{m}$ , where $p$ is a fixed odd prime,…

math.NT2023

Multiple exponential sums and their applications to quadratic congruences

Nilanjan Bag, Stephan Baier, Anup Haldar

In this paper, we develop a method of evaluating general exponential sums with rational amplitude functions for multiple variables which complements works by T. Cochrane and Z. Zhe…

math.NT2023

Fourth power mean of the general $s$ -dimensional Kloosterman sum mod $p$

Nilanjan Bag, Anup Haldar

In this article, we prove an asymptotic formula for the fourth power mean of a general $s$ -dimensional hyper-Kloosterman sum. We find the number of solutions of certain congruence…

math.NT2023

Equidistribution of Solutions of Ternary Quadratic Congruences Modulo Prime Powers

Anup Haldar

Let $p$ be a fixed odd prime and $Q (x, y, z) = a x^{2} + b x y + c y^{2} + d x z + ey z + f z^{2}$ be a fixed quadratic form in $Z [x, y, z]$ which is non-degenerate in $F_{p} [x, y, z]$ and $(a(4ac…

math.NT2022

Asymptotic behavior of small solutions of quadratic congruences in three variables modulo prime powers

Stephan Baier, Anup Haldar

Let $p > 5$ be a fixed prime and assume that $α_{1}, α_{2}, α_{3}$ are coprime to $p$ . We study the asymptotic behavior of small solutions of congruences of the form $α_1x_1^2+α_2x_2^2+α_3x_…

math.NT2022

Small Pythagorean triples modulo prime powers

Stephan Baier, Anup Haldar

Let $p > 5$ be a fixed prime. We obtain an asymptotic formula related to small solutions of quadratic congruences of the form $x_{1}^{2} + x_{2}^{2} \equiv x_{3}^{2} mod p^{n}$ where $\max\{|x_1|,|…

Small solutions to inhomogeneous and homogeneous quadratic congruences modulo prime powers

Multiple exponential sums and their applications to quadratic congruences

Fourth power mean of the general s-dimensional Kloosterman sum mod p

Equidistribution of Solutions of Ternary Quadratic Congruences Modulo Prime Powers

Asymptotic behavior of small solutions of quadratic congruences in three variables modulo prime powers

Small Pythagorean triples modulo prime powers

Fourth power mean of the general $s$ -dimensional Kloosterman sum mod $p$