Haruka Sakai

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math.NT2026

On a Turán's theorem for arithmetic progressions

T. Makoto Minamide, Haruka Sakai, Yoshio Tanigawa

Let $m \geq 1$ be a fixed integer, $a$ an integer satisfying $(a, m) = 1$ , and $z \geq 1$ a real parameter. Denote by $ω_{z} (n; m, a)$ the number of distinct prime divisors $p$ of $n$ sat…

math.NT2026

On a Turán's theorem for small primes

T. Makoto Minamide, Haruka Sakai, Yoshio Tanigawa

Denote by $ω (n)$ the number of distinct prime divisors of the natural number $n$ . In 2007, Granville and Soundararajan gave a quite new method to compute the higher moments $\sum_{…