Analytic Number Theory Research

We introduce a method for showing that there exist prime numbers which are very close together. The method depends on the level of distribution of primes in arithmetic progressions. Assuming the Elliott-Halberstam conjecture, we prove that there are infinitely often primes differing by 16 or less. Even a much weaker c…

• CEM YALÇIN YILDIRIM

No abstract yet.

• HACER ÖZDEN AYNA

No abstract yet.

• SERKAN ARACI

We consider weighted q‐Genocchi numbers and polynomials. We investigated some interesting properties of the weighted q‐Genocchi numbers related to weighted q‐Bernstein polynomials by using fermionic p‐adic integrals on ℤp.

• SERKAN ARACI

The main purpose of this paper is to construct generating functions for some families of Genocchi type polynomials. By applying the derivative operator to these generating functions, we define a function which interpolates these polynomials at negative integers. Among other results, we prove a multiplication theorem f…

• BURAK KURT

The aim of this paper, firstly, is to construct generating functions of q‐Euler numbers and polynomials of higher order by applying the fermionic p‐adic q‐Volkenborn integral, secondly, to define multivariate q‐Euler zeta function (Barnes‐type Hurwitz q‐Euler zeta function) and l‐function which interpolate these numbe…

• İSMAİL NACİ CANGÜL

The aim of this paper, firstly, is to construct generating functions of q‐Euler numbers and polynomials of higher order by applying the fermionic p‐adic q‐Volkenborn integral, secondly, to define multivariate q‐Euler zeta function (Barnes‐type Hurwitz q‐Euler zeta function) and l‐function which interpolate these numbe…

• İSMAİL NACİ CANGÜL
• YILMAZ ŞİMŞEK

Abstract We introduce a family of algebraic curves over 𝔽 q 2n (for an odd n) and show that they are maximal. When n = 3, our curve coincides with the 𝔽 q 6 -maximal curve that has been found by Giulietti and Korchmáros recently. Their curve (i.e., the case n = 3) is the first example of a maximal curve proven not to…

No abstract yet.

• AYHAN DİL

We prove that $ \mathop{ \lim \inf}\limits_{n \rightarrow \infty} \frac{p_{n+1}-p_{n}}{\sqrt{\log p_{n}} \left(\log \log p_{n}\right)^{2}}< \infty, $where pn denotes the nth prime. Since on average pn+1−pn is asymptotically log n, this shows that we can always find pairs of primes much closer together than the average…

• CEM YALÇIN YILDIRIM

This paper presents an improved Plantard’s modular arithmetic (Plantard arithmetic) tailored for Lattice-Based Cryptography (LBC). Based on the improved Plantard arithmetic, we present faster implementations of two LBC schemes, Kyber and NTTRU, running on Cortex-M4. The intrinsic advantage of Plantard arithmetic is th…

• ÇETİN KAYA KOÇ

In the preprint [3], Goldston, Pintz, and Yıldırım established, among other things, \begin{equation} \liminf_{n\to\infty}{p_{n+1}-p_n\over\log p_n}=0, \end{equation} with $p_n$ the $n$th prime. In the present article, which is essentially self-contained, we shall develop a simplified account of the method used in [3].…

• CEM YALÇIN YILDIRIM