Asaf Cohen Antonir

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math.NT2022

An Elementary Proof of a Theorem of Hardy and Ramanujan

Asaf Cohen Antonir, Asaf Shapira

Let $Q (n)$ denote the number of integers $1 \leq q \leq n$ whose prime factorization $q = \prod_{i = 1}^{t} p_{i}^{a_{i}}$ satisfies $a_{1} \geq a_{2} \geq \dots \geq a_{t}$ . Hardy and Ramanujan…

math.NT2021

On Erdős's Method for Bounding the Partition Function

Asaf Cohen Antonir, Asaf Shapira

For fixed $m$ and $R \subseteq {0, 1, \dots, m - 1}$ , take $A$ to be the set of positive integers congruent modulo $m$ to one of the elements of $R$ , and let $p_{A} (n)$ be the number of…