Muhammet Boran

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20232026

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math.NT2026

Improved Averaged Distribution of $d_{3} (n)$ in Prime Arithmetic Progressions

Metin Can Aydemir, Muhammet Boran

We say that $d_{3} (n)$ has exponent of distribution $θ$ if, for every $ε > 0$ , the expected asymptotic holds uniformly for all moduli $q \leq x^{θ - ε}$ . Nguyen proved…

math.NT2023

Sums of Powers of Primes in Arithmetic Progression

Muhammet Boran, John Byun, Zhangze Li +2

Gerard and Washington proved that, for $k > - 1$ , the number of primes less than $x^{k + 1}$ can be well approximated by summing the $k$ -th powers of all primes up to $x$ . We extend t…

Improved Averaged Distribution of d3​(n) in Prime Arithmetic Progressions

Sums of Powers of Primes in Arithmetic Progression

Improved Averaged Distribution of $d_{3} (n)$ in Prime Arithmetic Progressions