Bikram Misra

collaborators

4 papers

math.NT2026

On existence of generalised Lehmer numbers modulo primes

Bikram Misra, Bidisha Roy, B. Sury

In this article, we discuss a multivariable analogue of Lehmer's parity problem. We generalise the notions of Lehmer numbers as Lehmer $q$ -tuples for a fixed odd prime $q$ . We coun…

math.NT2025

Triple convolution sums of the generalised divisor functions and related sums over primes

Bikram Misra, Biswajyoti Saha

We study the triple convolution sum of the generalised divisor functions $n \leq x \sum d_{k} (n + h) d_{l} (n) d_{m} (n - h),$ where $h \leq x^{1 - ε}$ for any $ε > 0$ and $d_{k} (n)$ denotes the gen…

math.NT2025

A triple convolution sum of the divisor function

Bikram Misra, M. Ram Murty, Biswajyoti Saha

We study the triple convolution sum of the divisor function given by $n \leq x \sum d (n) d (n - h) d (n + h)$ for $h \neq = 0$ and $d (n)$ denotes the number of positive divisors of $n$ . Ba…

math.NT2025

On additive convolution sum of arithmetic functions and related questions

Bikram Misra, Biswajyoti Saha, Anubhav Sharma

Ingham studied two types of convolution sums of the divisor function, the shifted convolution sum $\sum_{n \leq N} d (n) d (n + h)$ and the additive convolution sum $\sum_{n < N} d(n) d…