Sarvagya Jain

collaborators

4 papers

math.NT2026

Error Term Estimates for Sets of Remainders

Omkar Baraskar, Prashant Gokhale, Sarvagya Jain +1

For a positive integer $n$ , let $S_{1} (n) = {n mod k : 1 \leq k \leq ⌊ n /2 ⌋}, s_{1} (n) = ∣ S_{1} (n) ∣.$ Baraskar and Vukusic proved $s_{1} (n) = Ξ n + O (n / (lo g n lo g lo g n))$ for…

math.NT2026

Asymptotic Behavior of Iterated Sets of Remainders

Omkar Baraskar, Prashant Gokhale, Sarvagya Jain +1

For a positive integer $n$ , let $S_{0} (n) = {1, 2, \dots, ⌊ n /2 ⌋}, S_{j + 1} (n) = {n mod k : k \in S_{j} (n) ∖ {0}},$ and put $s_{j} (n) := ∣ S_{j} (n) ∣$ . The sets define…

math.NT2025

Additive Problems with Primes from a Thin Bohr Set

Sarvagya Jain

For an irrational $α \in R$ , we consider additive problems with the set of primes satisfying $∥ α p ∥ \leq \frac{1}{p ^{τ}}$ for some fixed $τ > 0$ . In particular, we show…

math.NT2025

Smooth Numbers in Short Intervals

Sarvagya Jain

Let $ X \geq y \geq 2 $, and let $ u = \frac{\log X}{\log y} $. We say a number is \textit{ $y$ -smooth} if all of its prime factors are less than or equal to $ y $. In this pa…