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
Citation Format
BibTeX
@article{goral2026infinitude,
author = {G{\"o}ral, Haydar and Ad{\i}belli, Azem Berivan},
title = {The infinitude of primes and some coloring theorems},
journal = {Amer. Math. Monthly},
year = {2026}
}
Citation Format
BibTeX
@article{goral2024variants,
author = {G{\"o}ral, Haydar and B{\"u}y{\"u}ka{\c{s}}{\i}k, Engin and Sertba{\c{s}}, Do{\u{g}}a Can},
title = {A note on variants of {E}uler's $\varphi$-function},
journal = {Publicationes Mathematicae Debrecen},
volume = {105},
number = {1-2},
pages = {67--89},
year = {2024}
}
Citation Format
BibTeX
@article{goral2023eulerzagier,
author = {G{\"o}ral, Haydar and {\c{S}}ermin {\c{C}}am {\c{C}}elik},
title = {Euler--{Z}agier sums via trigonometric series},
journal = {Mathematical Reports},
volume = {25 (75)},
number = {3},
pages = {381--412},
year = {2023}
}
Citation Format
BibTeX
@article{goral2023arithmetic,
author = {G{\"o}ral, Haydar and Eyido{\u{g}}an, Sad{\i}k and Kutlu, Mustafa Kutay},
title = {Arithmetic progressions in certain subsets of finite fields},
journal = {Finite Fields and Their Applications},
volume = {91},
pages = {102264},
month = {October},
year = {2023}
}
Citation Format
BibTeX
@article{goral2023classification,
author = {G{\"o}ral, Haydar and {\c{S}}ermin {\c{C}}am {\c{C}}elik and Eyido{\u{g}}an, Sad{\i}k and Sertba{\c{s}}, Do{\u{g}}a Can},
title = {On classification of sequences containing arbitrarily long arithmetic progressions},
journal = {Int. J. of Number Theory},
volume = {19},
number = {08},
pages = {1917--1952},
year = {2023}
}
Citation Format
BibTeX
@article{goral2023irreducibility,
author = {G{\"o}ral, Haydar and Batal, Ahmet and Eyido{\u{g}}an, Sad{\i}k},
title = {Irreducibility and primality in differentiability classes},
journal = {Real Analysis Exchange},
volume = {48},
number = {1},
pages = {119--138},
year = {2023}
}
Citation Format
BibTeX
@article{goral2023greentao,
author = {G{\"o}ral, Haydar and {\"O}zcan, Hikmet Burak and Sertba{\c{s}}, Do{\u{g}}a Can},
title = {The {G}reen--{T}ao theorem and the infinitude of primes in domains},
journal = {Amer. Math. Monthly},
volume = {130},
number = {2},
year = {2023}
}
Citation Format
BibTeX
@article{goral2022class,
author = {G{\"o}ral, Haydar},
title = {Class number and the special values of {L}-functions},
journal = {Math. Reports},
volume = {24 (74)},
number = {4},
pages = {693--701},
year = {2022}
}
Citation Format
BibTeX
@article{goral2022hyperharmonic,
author = {G{\"o}ral, Haydar and Altunta{\c{s}}, {\c{C}}a{\u{g}}atay and Sertba{\c{s}}, Do{\u{g}}a Can},
title = {The difference of hyperharmonic numbers via geometric and analytic methods},
journal = {J. Korean Math. Soc.},
volume = {59},
number = {6},
pages = {1103--1137},
year = {2022}
}
Citation Format
BibTeX
@article{goral2022lehmer,
author = {G{\"o}ral, Haydar},
title = {Lehmer's conjecture via model theory},
journal = {Proc. Japan Acad. Ser. A Math. Sci.},
volume = {98},
number = {7},
pages = {52--55},
year = {2022}
}
Citation Format
BibTeX
@article{goral2022harmonic,
author = {G{\"o}ral, Haydar},
title = {Some remarks on harmonic type matrices},
journal = {Integers},
volume = {22},
pages = {Paper No. A66},
year = {2022}
}
Citation Format
BibTeX
@article{goral2021dedekind,
author = {G{\"o}ral, Haydar and Altunta{\c{s}}, {\c{C}}a{\u{g}}atay},
title = {Dedekind harmonic numbers},
journal = {Proc. Indian Acad. Sci. (Math. Sci.)},
volume = {131},
number = {2},
pages = {Paper No. 46},
year = {2021}
}
Citation Format
BibTeX
@article{goral2021bernoulli,
author = {G{\"o}ral, Haydar and Sertba{\c{s}}, Do{\u{g}}a Can},
title = {Applications of class numbers and {B}ernoulli numbers to harmonic type sums},
journal = {Bull. Korean Math. Soc.},
volume = {58},
number = {6},
pages = {1463--1481},
year = {2021}
}
Citation Format
BibTeX
@article{goral2021algebraic,
author = {G{\"o}ral, Haydar and {\c{S}}ermin {\c{C}}am {\c{C}}elik},
title = {A note on points on algebraic sets},
journal = {Hacet. J. Math. Stat.},
volume = {50},
number = {3},
pages = {821--824},
year = {2021}
}
Citation Format
BibTeX
@article{goral2021numberfields,
author = {G{\"o}ral, Haydar and {\c{S}}ermin {\c{C}}am {\c{C}}elik},
title = {Number fields and divisible groups via model theory},
journal = {Turkish Journal of Mathematics},
volume = {45},
pages = {220--232},
year = {2021}
}
Citation Format
BibTeX
@article{goral2020infinitude_novel,
author = {G{\"o}ral, Haydar and {\"O}zcan, Hikmet Burak},
title = {Several novel proofs of the infinitude of primes},
journal = {The Mathematics Student},
volume = {89},
number = {3-4},
pages = {91--95},
year = {2020}
}
Citation Format
BibTeX
@article{goral2020nonintegerness,
author = {G{\"o}ral, Haydar and Sertba{\c{s}}, Do{\u{g}}a Can},
title = {Euler Sums and Non-integerness of Harmonic Type Sums},
journal = {Hacet. J. Math. Stat.},
volume = {49},
number = {2},
pages = {586--598},
year = {2020}
}
Citation Format
BibTeX
@article{goral2020padic,
author = {G{\"o}ral, Haydar},
title = {$p$-adic metrics and the infinitude of primes},
journal = {Mathematics Magazine},
volume = {93},
year = {2020},
number = {1},
pages = {19--22}
}
Citation Format
BibTeX
@article{goral2020dirichlet,
author = {G{\"o}ral, Haydar and {\c{S}}ermin {\c{C}}am {\c{C}}elik},
title = {Approximation by Special Values of {D}irichlet Series},
journal = {Proc. Amer. Math. Soc.},
volume = {148},
number = {1},
pages = {83--93},
year = {2020}
}
Citation Format
BibTeX
@article{goral2019divisor,
author = {G{\"o}ral, Haydar},
title = {Divisor Function and Bounds in Domains with Enough Primes},
journal = {Hacet. J. Math. Stat.},
volume = {48},
number = {2},
pages = {399--405},
year = {2019}
}
Citation Format
BibTeX
@article{goral2019smallheight,
author = {G{\"o}ral, Haydar},
title = {Algebraic Numbers with Elements of Small Height},
journal = {Math. Logic Quart.},
volume = {65},
number = {1},
pages = {14--22},
year = {2019}
}
Citation Format
BibTeX
@article{goral2019tame,
author = {G{\"o}ral, Haydar},
title = {Tame Expansions of $\omega$-Stable Theories and Definable Groups},
journal = {Notre Dame Journal of Formal Logic},
volume = {60},
number = {2},
pages = {161--194},
year = {2019}
}
Citation Format
BibTeX
@inproceedings{goral2019nullstellensatz_notes,
author = {G{\"o}ral, Haydar},
title = {Nullstellensatz via Nonstandard Methods},
booktitle = {Notes from the International Autumn School on Computational Number Theory},
pages = {313--322},
year = {2019}
}
Citation Format
BibTeX
@article{goral2019fractions,
author = {G{\"o}ral, Haydar and Sertba{\c{s}}, Do{\u{g}}a Can},
title = {Density and Finiteness Results on Sums of Fractions},
journal = {Proc. Amer. Math. Soc.},
volume = {147},
number = {2},
pages = {567--581},
year = {2019}
}
Citation Format
BibTeX
@article{goral2018height,
author = {G{\"o}ral, Haydar},
title = {Height Bounds, Nullstellensatz and Primality},
journal = {Communications in Algebra},
volume = {46},
number = {10},
pages = {4463--4472},
year = {2018}
}
Citation Format
BibTeX
@article{goral2018rare_integers,
author = {G{\"o}ral, Haydar and Alkan, Emre and Sertba{\c{s}}, Do{\u{g}}a Can},
title = {Hyperharmonic numbers can rarely be integers},
journal = {Integers},
volume = {18},
pages = {Paper No. A43},
year = {2018}
}
Citation Format
BibTeX
@article{goral2018congruence,
author = {G{\"o}ral, Haydar and Sertba{\c{s}}, Do{\u{g}}a Can},
title = {A congruence for some generalized harmonic type sums},
journal = {Int. J. of Number Theory},
volume = {14},
number = {4},
pages = {1033--1046},
year = {2018}
}
Citation Format
BibTeX
@article{goral2018mann,
author = {G{\"o}ral, Haydar},
title = {Interpretable Groups in {M}ann Pairs},
journal = {Archive for Mathematical Logic},
number = {3-4},
pages = {203--237},
year = {2018}
}
Citation Format
BibTeX
@article{goral2018ramanujan,
author = {G{\"o}ral, Haydar and Alkan, Emre},
title = {Structural properties of {D}irichlet series with harmonic coefficients},
journal = {The Ramanujan Journal},
volume = {45},
number = {2},
pages = {569--600},
year = {2018}
}
Citation Format
BibTeX
@article{goral2018acta,
author = {G{\"o}ral, Haydar and Sertba{\c{s}}, Do{\u{g}}a Can},
title = {Divisibility properties of hyperharmonic numbers},
journal = {Acta Mathematica Hungarica},
volume = {154},
number = {1},
pages = {147--186},
year = {2018}
}
Citation Format
BibTeX
@article{goral2017trig,
author = {G{\"o}ral, Haydar and Alkan, Emre},
title = {Trigonometric series and special values of {L}-functions},
journal = {J. Number Theory},
volume = {178},
pages = {94--117},
year = {2017}
}
Citation Format
BibTeX
@article{goral2017hyper_not_int,
author = {G{\"o}ral, Haydar and Sertba{\c{s}}, Do{\u{g}}a Can},
title = {Almost all hyperharmonic numbers are not integers},
journal = {J. Number Theory},
volume = {171},
pages = {495--526},
year = {2017}
}
Citation Format
BibTeX
@article{goral2013mobius,
author = {G{\"o}ral, Haydar and Alkan, Emre},
title = {On Sums over the {M}{\"o}bius function and Discrepancy of Fractions},
journal = {J. Number Theory},
volume = {133},
number = {7},
pages = {2217--2239},
year = {2013}
}