Jewel Mahajan

activity

20242026

collaborators

6 papers

math.NT2026

Shifted convolution sums of coefficients of symmetric power $L$ -functions with $k$ -full kernels over sums of squares in arithmetic progressions

Jewel Mahajan, Arnab Mitra

Let $q$ be an integer and let $f$ be a normalised Hecke eigenform of integral weight for the full modular group. Let $L (s, sym^{j} f)$ denote the $j$ -th symmetric power $L$ -f…

math.NT2026

Moments and sign changes of symmetric power $L$ -function coefficients over sums of squares

Jewel Mahajan, Arnab Mitra

Let $f$ be a normalised Hecke eigenform of even integral weight for the full modular group $SL (2, Z)$ , let $L (s, sym^{j} f)$ be the $j$ th symmetric power $L…

math.NT2026

Multiplicative functions additive on partitions of $2 k$ nonzero squares

Jewel Mahajan

For a fixed integer $k \geq 3$ , we study the multiplicative functions $f : N \to C$ satisfying \[ f\Bigl(\sum_{i=1}^{2k} x_i^2\Bigr) = \sum_{j=1}^{k} f\bigl(x_{2j…

math.NT2026

Weighted Fruit Diophantine Equations and Hyperelliptic Curves

Jewel Mahajan, Apeksha Sanghi

We study the weighted fruit Diophantine equation $a x^{d} - c (m^{2} y^{2} + n^{2} z^{2}) + x y z - b = 0$ , generalising previous work by Majumdar--Sury, Vaishya--Sharma, and Pra…

math.NT2025

The metric theory of small gaps for a sequence of real numbers

Jewel Mahajan

Let $(a_{n})_{n \geq 1}$ be a sequence of distinct positive integers. The metric theory of minimal gaps for the sequence ${α a_{n} mod 1, 1 \leq n \leq N}$ as $N \to \infty$ wa…

math.NT2024

A lower bound for classical Kloosterman sums and an application

Stephan Baier, Jishu Das, Jewel Mahajan

We present a lower bound for the classical Kloosterman sum $S (a, b; c)$ where $(ab, c) = 1$ and $c$ is an odd integer. We apply this lower bound for Kloosterman sums to derive an explic…

Shifted convolution sums of coefficients of symmetric power L-functions with k-full kernels over sums of squares in arithmetic progressions

Moments and sign changes of symmetric power L-function coefficients over sums of squares

Multiplicative functions additive on partitions of 2k nonzero squares

Weighted Fruit Diophantine Equations and Hyperelliptic Curves

The metric theory of small gaps for a sequence of real numbers

A lower bound for classical Kloosterman sums and an application

Shifted convolution sums of coefficients of symmetric power $L$ -functions with $k$ -full kernels over sums of squares in arithmetic progressions

Moments and sign changes of symmetric power $L$ -function coefficients over sums of squares

Multiplicative functions additive on partitions of $2 k$ nonzero squares