Kunjakanan Nath

activity

20242026

collaborators

5 papers

math.NT2026

Diophantine approximation with integers having no large prime factors

Kunjakanan Nath, Habibur Rahaman

Given any irrational number $I^\pm$ , we show that for any $0 < I^¸ < 6/17$ , there are infinitely many $y$ -smooth (friable) numbers $n$ such that $∥ n I^\pm ∥ < n^{- I^¸},$ where $(\log n)^C\le…

math.NT2026

Real zeros of $L^{'} (s, I ¨ _{d})$

Youness Lamzouri, Kunjakanan Nath

In 1990, Baker and Montgomery conjectured that $L^{'} (s, I ¨ _{d})$ has $≍ lo g lo g ∣ d ∣$ real zeros in the interval $[1/2, 1]$ for almost all fundamental discriminants $d$ . The study o…

math.NT2025

On binary correlations of Fourier coefficients of holomorphic cusp forms at prime arguments

Jiseong Kim, Kunjakanan Nath

Let ${I^»_{f} (n)}_{n \geq 1}$ be the normalized Hecke eigenvalues of a given holomorphic cusp form $f$ of even weight $k$ . We show under the assumption of the existence of Littlewoo…

math.NT2025

Almost primes and primes that are sums of two squares plus 1

Kunjakanan Nath, Likun Xie

In this paper, we obtain a lower bound for the number of primes $p \leq x$ such that $p - 1$ is a sum of two squares and $p + 2$ has a bounded number of prime factors. The proof uses th…

math.NT2024

The distribution of the maximum of cubic character sums