Publications & Research

Papers

2026

Box progressions, abelian power-free morphisms and a sieve technique for the template method

Mathematics of Computation (to appear)
with Sadık Eyidoğan and Nihan Tanısalı
2026

The infinitude of primes and some coloring theorems

Amer. Math. Monthly
with Azem Berivan Adıbelli
2024

A note on variants of Euler's $\varphi$-function

Publicationes Mathematicae Debrecen, 105 (1-2), 67--89
with Engin Büyükaşık and Doğa Can Sertbaş
2023

Euler–Zagier sums via trigonometric series

Mathematical Reports, 25 (75), no. 3, 381--412
with Şermin Çam Çelik
2023

Arithmetic progressions in certain subsets of finite fields

Finite Fields and Their Applications, 91, 102264
with Sadık Eyidoğan and Mustafa Kutay Kutlu
2023

On classification of sequences containing arbitrarily long arithmetic progressions

Int. J. of Number Theory, 19 (08), 1917--1952
with Şermin Çam Çelik, Sadık Eyidoğan and Doğa Can Sertbaş
2023

Irreducibility and primality in differentiability classes

Real Analysis Exchange, 48 (1), 119--138
with Ahmet Batal and Sadık Eyidoğan
2023

The Green–Tao theorem and the infinitude of primes in domains

Amer. Math. Monthly, 130 (2)
with Hikmet Burak Özcan and Doğa Can Sertbaş
2022

Class number and the special values of L-functions

Math. Reports, 24 (74), no. 4, 693--701
2022

The difference of hyperharmonic numbers via geometric and analytic methods

J. Korean Math. Soc., 59 (6), 1103--1137
with Çağatay Altuntaş and Doğa Can Sertbaş
2022

Lehmer's conjecture via model theory

Proc. Japan Acad. Ser. A Math. Sci., 98 (7), 52--55
2022

Some remarks on harmonic type matrices

Integers, 22, Paper No. A66
2021

Dedekind harmonic numbers

Proc. Indian Acad. Sci. (Math. Sci.), 131 (2), Paper No. 46
with Çağatay Altuntaş
2021

Applications of class numbers and Bernoulli numbers to harmonic type sums

Bull. Korean Math. Soc., 58 (6), 1463--1481
with Doğa Can Sertbaş
2021

A note on points on algebraic sets

Hacet. J. Math. Stat., 50 (3), 821--824
with Şermin Çam Çelik
2021

Number fields and divisible groups via model theory

Turkish Journal of Mathematics, 45, 220--232
with Şermin Çam Çelik
2020

Several novel proofs of the infinitude of primes

The Mathematics Student, 89 (3-4), 91--95
with Hikmet Burak Özcan
2020

Euler Sums and Non-integerness of Harmonic Type Sums

Hacet. J. Math. Stat., 49 (2), 586--598
with Doğa Can Sertbaş
2020

$p$-adic metrics and the infinitude of primes

Mathematics Magazine, 93 (1), 19--22
2020

Approximation by Special Values of Dirichlet Series

Proc. Amer. Math. Soc., 148 (1), 83--93
with Şermin Çam Çelik
2019

Divisor Function and Bounds in Domains with Enough Primes

Hacet. J. Math. Stat., 48 (2), 399--405
2019

Algebraic Numbers with Elements of Small Height

Math. Logic Quart., 65 (1), 14--22
2019

Tame Expansions of $\omega$-Stable Theories and Definable Groups

Notre Dame Journal of Formal Logic, 60 (2), 161--194
2019

Nullstellensatz via Nonstandard Methods

Notes from the International Autumn School on Computational Number Theory, 313--322
2019

Density and Finiteness Results on Sums of Fractions

Proc. Amer. Math. Soc., 147 (2), 567--581
with Doğa Can Sertbaş
2018

Height Bounds, Nullstellensatz and Primality

Communications in Algebra, 46 (10), 4463--4472
2018

Hyperharmonic numbers can rarely be integers

Integers, 18, Paper No. A43
with Emre Alkan and Doğa Can Sertbaş
2018

A congruence for some generalized harmonic type sums

Int. J. of Number Theory, 14 (4), 1033--1046
with Doğa Can Sertbaş
2018

Interpretable Groups in Mann Pairs

Archive for Mathematical Logic, (3-4), 203--237
2018

Structural properties of Dirichlet series with harmonic coefficients

The Ramanujan Journal, 45 (2), 569--600
with Emre Alkan
2018

Divisibility properties of hyperharmonic numbers

Acta Mathematica Hungarica, 154 (1), 147--186
with Doğa Can Sertbaş
2017

Trigonometric series and special values of L-functions

J. Number Theory, 178, 94--117
with Emre Alkan
2017

Almost all hyperharmonic numbers are not integers

J. Number Theory, 171, 495--526
with Doğa Can Sertbaş
2013

On Sums over the Möbius function and Discrepancy of Fractions

J. Number Theory, 133 (7), 2217--2239
with Emre Alkan

Submitted Research Papers and Preprints

Submitted

Roth's theorem for certain subsets of finite rings

submitted
with Sadık Eyidoğan and Mustafa Kutay Kutlu
Submitted

Some Goldbach Properties for Polynomials and Formal Power Series

submitted
with Sinem Benli-Göral and Mustafa Kutay Kutlu
Submitted

Harmonic progressions in additive combinatorics: van der Waerden, Szemerédi and Green--Tao analogs

submitted
with Şermin Çam Çelik and Doğa Can Sertbaş
Preprint

On sequences which contain various progressions

to be submitted
with Ahmet Batal, Şermin Çam Çelik and Doğa Can Sertbaş

Other Publications and Popular Mathematics

2025

A problem proposal to the American Mathematical Monthly

Published in 2025 March
2020

Egyptian fractions

Matematik Dünyası Journal
2020

Some Results on Harmonic Type Sums

Duzce University Journal of Science and Technology, 8, 642--653
with Doğa Can Sertbaş
2014

Plato, Cosmology and Mathematics

Fasikül Dergisi
with Irem Portakal
2012

Bertrand Postulate and the Distribution of Prime Numbers

Matematik Dünyası Journal
with Barış Paksoy
2009-2012

Beyincik and Eureka!, brain teasers

Columns in Matematik Dünyası Journal
2006-Present

Chess column

Several times since 2006, Matematik Dünyası Journal