arXiv subjects

Ahmet M. Guloglu

Publications and source records attributed to Ahmet M. Guloglu.

3 recordsLinked to original sources

arXiv2008

On primitive Dirichlet characters and the Riemann hypothesis

For any natural number $n$, let $X'_n$ be the set of primitive Dirichlet characters modulo $n$. We show that if the Riemann hypothesis is true, then the inequality $|X'_{2n_k}|\le C_2 e^{-γ} ϕ(2n_k)/\log\log(2n_k)$ holds for all $k\ge 1$, where $n_k$ is the product of the first $k$ primes, $γ$ is the Euler-Mascheroni constant, $C_2$ is the twin prime constant, and $ϕ(n)$ is the Euler function. On the other hand, if the Riemann hypothesis is false, then there are infinitely many $k$ for which the same inequality holds and infinitely many $k$ for which it fails to hold.

math.NT↗

arXiv2008

Sums with multiplicative functions over a Beatty sequence

We study sums with multiplicative functions that take values over a non-homogenous Beatty sequence. We then apply our result in a few special cases to obtain asymptotic formulas such as the number of integers in a Beatty sequence representable as a sum of two squares up to a given magnitude.

math.NT↗

arXiv2007

Representations of integers as sums of primes from a Beatty sequence

We study the problem of representing integers as sums of prime numbers from a fixed Beatty sequence $B_{α,β}$, where $α>1$ is irrational and of finite type.

math.NT↗