Omkar Baraskar

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20242026

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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

Bounds for sets of remainders

Omkar Baraskar, Ingrid Vukusic

Let $s (n)$ be the number of different remainders $n mod k$ , where $1 \leq k \leq ⌊ n /2 ⌋$ . This rather natural sequence is sequence A283190 in the OEIS and while some…