Göral, Haydar
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Göral, H.
Goral, H.
Goral, Haydar
Goral, H.
Goral, Haydar
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haydargoral@iyte.edu.tr
Main Affiliation
04.02. Department of Mathematics
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Current Staff
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Documents
32
Citations
53
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4
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Scholarly Output
16
Articles
15
Views / Downloads
59658/2367
Supervised MSc Theses
1
Supervised PhD Theses
0
WoS Citation Count
8
Scopus Citation Count
7
Patents
0
Projects
1
WoS Citations per Publication
0.50
Scopus Citations per Publication
0.44
Open Access Source
6
Supervised Theses
1
| Journal | Count |
|---|---|
| Mathematical Reports | 2 |
| American Mathematical Monthly | 2 |
| Finite Fields and their Applications | 1 |
| Hacettepe Journal of Mathematics and Statistics | 1 |
| Integers | 1 |
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16 results
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Now showing 1 - 10 of 16
Article Lehmer’s Conjecture Via Model Theory(Japan Academy, 2022) Göral, HaydarIn this short note, we study Lehmer's conjecture in terms of stability theory. We state Bounded Lehmer's conjecture, and we prove that if a certain formula is uniformly stable in a class of structures, then Bounded Lehmer's conjecture holds. Our proof is based on Van der Waerden's theorem from additive combinatoricsArticle Citation - WoS: 2Citation - Scopus: 1The Difference of Hyperharmonic Numbers Via Geometric and Analytic Methods(Korean Mathematical Society, 2022) Altuntaş, Çağatay; Göral, Haydar; Sertbaş, Doğa CanOur motivation in this note is to find equal hyperharmonic numbers of different orders. In particular, we deal with the integerness property of the difference of hyperharmonic numbers. Inspired by finite-ness results from arithmetic geometry, we see that, under some extra assumption, there are only finitely many pairs of orders for two hyper-harmonic numbers of fixed indices to have a certain rational difference. Moreover, using analytic techniques, we get that almost all differences are not integers. On the contrary, we also obtain that there are infinitely many order values where the corresponding differences are integers.Article The Infinitude of the Primes and Some Coloring Theorems(Taylor & Francis inc, 2025) Adibelli, Azem Berivan; Goral, HaydarWe first prove the infinitude of the primes via a special case of Rado's theorem whose proof is based on the infinite Ramsey theorem. In the proof, we use the colorings of the positive integers introduced by Levent Alpoge [1] and Andrew Granville [2]. Finally, using Rado's theorem for integral domains, we will give another proof for the infinitude of nonassociated prime elements in any unique factorization domain R with a few units.Article Several Novel Proofs of the Infinitude of Primes(The Indian Mathematical Society, 2020) Göral,H.; Özcan,H.B.In this note, our aim is to provide several short proofs of the infinitude of primes, and we believe that the proofs have novelty value. © Indian Mathematical Society, 2020.Article Citation - WoS: 1Citation - Scopus: 1Irreducibility and Primality in Differentiability Classes(Michigan State University Press, 2023) Batal, Ahmet; Eyidoğan, S.; Göral, HaydarIn this note, we give criteria for the irreducibility of functions in Cm [0, 1], where m ∈ {1, 2, 3, ...} ∪ {∞} ∪ {ω}. We also discuss irreducibility in multivariable differentiability classes. Moreover, we characterize irreducible functions and maximal ideals in C∞ [0, 1]. In fact, irreducible and prime smooth functions are the same, and every maximal ideal of C∞ [0, 1] is principal. © 2023 Michigan State University Press. All rights reserved.Article A Note on Variants of Euler's Φ-Function(Univ debrecen, inst Mathematics, 2024) Buyukasik, Engin; Goral, Haydar; Sertbas, Doga CanIt is well-known that the sum of the firstnconsecutive integers alwaysdivides thek-th power sum of the firstnconsecutive integers whenkis odd. Motivatedby this result, in this note, we study the divisibility properties of the power sum ofpositive integers that are coprime tonand not surpassingn. First, we prove a finitenessresult for our divisibility sets using smooth numbers in short intervals. Then, we findthe exact structure of a certain divisibility set that contains the orders of these powersums and our result is of computational flavour.Article Citation - WoS: 2Citation - Scopus: 3The Green-Tao Theorem and the Infinitude of Primes in Domains(Taylor & Francis, 2022) Göral, Haydar; Özcan, Hikmet Burak; Sertbaş, Doğa CanWe first prove an elementary analogue of the Green-Tao Theorem. The celebrated Green-Tao Theorem states that there are arbitrarily long arithmetic progressions in the set of prime numbers. In fact, we show the Green-Tao Theorem for polynomial rings over integral domains with several variables. Using the Generalized Polynomial van der Waerden Theorem, we also prove that in an infinite unique factorization domain, if the cardinality of the set of units is strictly less than that of the domain, then there are infinitely many prime elements. Moreover, we deduce the infinitude of prime numbers in the positive integers using polynomial progressions of length three. In addition, using unit equations, we provide two more proofs of the infinitude of prime numbers. Finally, we give a new proof of the divergence of the sum of reciprocals of all prime numbers.Article Citation - WoS: 1Dedekind Harmonic Numbers(Indian Academy of Sciences, 2021) Altuntaş, Çağatay; Göral, HaydarFor any number field, we define Dedekind harmonic numbers with respect to this number field. First, we show that they are not integers except finitely many of them. Then, we present a uniform and an explicit version of this result for quadratic number fields. Moreover, by assuming the Riemann hypothesis for Dedekind zeta functions, we prove that the difference of two Dedekind harmonic numbers are not integers after a while if we have enough terms, and we prove the non-integrality of Dedekind harmonic numbers for quadratic number fields in another uniform way together with an asymptotic result.Master Thesis Classical Theorems of Ramsey Theory Via Combinatorial and Ultrafilter Methods(01. Izmir Institute of Technology, 2024) Adıbelli, Azem Berivan; Göral, HaydarBu tezde ana amaç, Ramsey teorisinin dört klasik teoremi olan Ramsey, Schur, van der Waerden ve Rado teoreminin ispatını sunmaktır. Bu teoremlerin birbirlerine denk olan sonlu ve sonsuz versiyonlarını ispatlarıyla birlikte ele alıyoruz. Ayrıca, filtreler olarak bilinen, standart olmayan analizin temel araçlarını tanıtıyoruz. Bunun yanı sıra, ultrafiltreler kullanılarak Schur teoreminin ve van der Waerden teoreminin özel bir durumunun iki farklı ispatını sunuyoruz.Article A Note on Points on Algebraic Sets(Hacettepe Üniversitesi, 2021) Çam Çelik, Şermin; Göral, HaydarIn this short note, we count the points on algebraic sets which lie in a subset of a domain. It is proved that the set of points on algebraic sets coming from certain subsets of a domain has the full asymptotic. This generalizes the first theorem of [E. Alkan and E.S. Yoruk, Statistics and characterization of matrices by determinant and trace, Ramanujan J., 2019] and also anwers some questions from the same article.