research | Giorgos N. Kapetanakis

I am interested in all aspects of finite fields (a.k.a. Galois fields) and their applications. If you are looking for a specific article and have no access to the corresponding journal, feel free to contact me.

You may want to check the cv section if you are interested in my volunteer service to the scientific community, such as journal or conference reviewing, conference or seminar organizing and so on.

journal articles

2026

Normal and primitive normal elements with prescribed traces in intermediate extensions of finite fields

Arpan Chandra Mazumder, Giorgos Kapetanakis, and Dhiren Kumar Basnet

Finite Fields and Their Applications, 2026

DOI arXiv Bib

@article{mazumderkapetanakisbasnet26,
  author = {Mazumder, Arpan Chandra and Kapetanakis, Giorgos and Basnet, Dhiren Kumar},
  title = {Normal and primitive normal elements with prescribed traces in intermediate extensions of finite fields},
  journal = {Finite Fields and Their Applications},
  volume = {110},
  number = {102745},
  pages = {14pp.},
  year = {2026},
  doi = {10.1016/j.ffa.2025.102745}
}

2025

Existence of special types of primitive pairs in finite fields avoiding affine hyperplanes

Himangshu Hazarika, Giorgos Kapetanakis, and Dhiren Kumar Basnet

Applicable Algebra in Engineering, Communication and Computing, 2025

DOI arXiv Bib

@article{hazarikakapetanakisbasnet25,
  author = {Hazarika, Himangshu and Kapetanakis, Giorgos and Basnet, Dhiren Kumar},
  title = {Existence of special types of primitive pairs in finite fields avoiding affine hyperplanes},
  journal = {Applicable Algebra in Engineering, Communication and Computing},
  volume = {to appear},
  year = {2025},
  doi = {10.1007/s00200-025-00698-2}
}

Normal points on Artin-Schreier curves over finite fields

Giorgos Kapetanakis and Lucas Reis

Comptes Rendus Mathématique, 2025

DOI arXiv Bib

@article{kapetanakisreis25,
  author = {Kapetanakis, Giorgos and Reis, Lucas},
  title = {Normal points on Artin-Schreier curves over finite fields},
  journal = {Comptes Rendus Mathématique},
  volume = {365},
  pages = {541--554},
  year = {2025},
  doi = {10.5802/crmath.740}
}

Fq-primitive points on varieties over finite fields

Soniya Takshak, Giorgos Kapetanakis, and Rajendra Kumar Sharma

Finite Fields and Their Applications, 2025

DOI arXiv Bib

@article{takshakkapetanakissharma25,
  author = {Takshak, Soniya and Kapetanakis, Giorgos and Sharma, Rajendra Kumar},
  title = {Fq-primitive points on varieties over finite fields},
  journal = {Finite Fields and Their Applications},
  volume = {103},
  number = {102582},
  year = {2025},
  pages = {8pp.},
  doi = {10.1016/j.ffa.2025.102582}
}

2024

The trace of primitive and 2-primitive elements in finite fields, revisited

Stephen D. Cohen and Giorgos Kapetanakis

Southeast Asian Bulletin of Mathematics, 2024

arXiv Bib HTML

@article{cohenkapetanakis24,
  author = {Cohen, Stephen D. and Kapetanakis, Giorgos},
  title = {The trace of primitive and 2-primitive elements in finite fields, revisited},
  journal = {Southeast Asian Bulletin of Mathematics},
  volume = {48},
  number = {2},
  pages = {161--184},
  year = {2024}
}

2023

Teaching perspectives of the Frobenius coin problem of two denominators

Giorgos Kapetanakis and Ioannis Rizos

The Teaching of Mathematics, 2023

DOI arXiv Bib

@article{kapetanakisrizos23b,
  author = {Kapetanakis, Giorgos and Rizos, Ioannis},
  title = {Teaching perspectives of the Frobenius coin problem of two denominators},
  journal = {The Teaching of Mathematics},
  volume = {XXVI},
  number = {2},
  pages = {57--67},
  year = {2023},
  doi = {10.57016/TM-BJZO1296}
}

2022

The existence of Fq-primitive points on curves using freeness

Stephen D. Cohen, Giorgos Kapetanakis, and Lucas Reis

Comptes Rendus Mathématique, 2022

DOI arXiv Bib

@article{cohenkapetanakisreis22,
  author = {Cohen, Stephen D. and Kapetanakis, Giorgos and Reis, Lucas},
  title = {The existence of Fq-primitive points on curves using freeness},
  journal = {Comptes Rendus Mathématique},
  volume = {360},
  pages = {641-652},
  year = {2022},
  doi = {10.5802/crmath.328}
}

On the existence of primitive normal elements of rational form over finite fields of even characteristic

Himangshu Hazarika, Dhiren Kumar Basnet, and Giorgos Kapetanakis

International Journal of Algebra and Computation, 2022

DOI arXiv Bib

@article{hazarikabasnetkapetanakis22,
  author = {Hazarika, Himangshu and Basnet, Dhiren Kumar and Kapetanakis, Giorgos},
  title = {On the existence of primitive normal elements of rational form over finite fields of even characteristic},
  journal = {International Journal of Algebra and Computation},
  volume = {32},
  number = {2},
  pages = {357--382},
  year = {2022},
  doi = {10.1142/S0218196722500187}
}

2021

Finite field extensions with the line or translate property for r-primitive elements

Stephen D. Cohen and Giorgos Kapetanakis

Journal of the Australian Mathematical Society, 2021

DOI arXiv Bib

@article{cohenkapetanakis21,
  author = {Cohen, Stephen D. and Kapetanakis, Giorgos},
  title = {Finite field extensions with the line or translate property for r-primitive elements},
  journal = {Journal of the Australian Mathematical Society},
  volume = {111},
  number = {3},
  pages = {313--319},
  year = {2021},
  doi = {10.1017/S1446788720000099}
}

2020

The translate and line properties for 2-primitive elements in quadratic extensions

Stephen D. Cohen and Giorgos Kapetanakis

International Journal of Number Theory, 2020

DOI arXiv Bib

@article{cohenkapetanakis20b,
  author = {Cohen, Stephen D. and Kapetanakis, Giorgos},
  title = {The translate and line properties for 2-primitive elements in quadratic extensions},
  journal = {International Journal of Number Theory},
  volume = {16},
  number = {9},
  pages = {2029--2040},
  year = {2020},
  doi = {10.1142/S1793042120501055}
}

The trace of 2-primitive elements of finite fields

Stephen D. Cohen and Giorgos Kapetanakis

Acta Arithmetica, 2020

DOI arXiv Bib

@article{cohenkapetanakis20a,
  author = {Cohen, Stephen D. and Kapetanakis, Giorgos},
  title = {The trace of 2-primitive elements of finite fields},
  journal = {Acta Arithmetica},
  volume = {192},
  number = {4},
  pages = {397-419},
  year = {2020},
  doi = {10.4064/aa190307-23-5}
}

2019

Further results on the Morgan-Mullen conjecture

Theodoulos Garefalakis and Giorgos Kapetanakis

Designs, Codes and Cryptography, 2019

DOI arXiv Bib HTML

@article{garefalakiskapetanakis19b,
  author = {Garefalakis, Theodoulos and Kapetanakis, Giorgos},
  title = {Further results on the Morgan-Mullen conjecture},
  journal = {Designs, Codes and Cryptography},
  volume = {87},
  number = {11},
  pages = {2639--2654},
  year = {2019},
  doi = {10.1007/s10623-019-00643-8}
}

A Swan-like note for a family of binary pentanomials

Giorgos Kapetanakis

Applicable Algebra in Engineering, Communication and Computing, 2019

DOI arXiv Bib HTML

@article{kapetanakis19,
  author = {Kapetanakis, Giorgos},
  title = {A Swan-like note for a family of binary pentanomials},
  journal = {Applicable Algebra in Engineering, Communication and Computing},
  volume = {30},
  number = {5},
  pages = {361--372},
  year = {2019},
  doi = {10.1007/s00200-018-0378-7}
}

Variations of the primitive normal basis theorem

Giorgos Kapetanakis and Lucas Reis

Designs, Codes and Cryptography, 2019

DOI arXiv Bib

@article{kapetanakisreis19,
  author = {Kapetanakis, Giorgos and Reis, Lucas},
  title = {Variations of the primitive normal basis theorem},
  journal = {Designs, Codes and Cryptography},
  volume = {87},
  number = {7},
  pages = {1459--1480},
  year = {2019},
  doi = {10.1007/s10623-018-0543-9}
}

On the existence of primitive completely normal bases of finite fields

Theodoulos Garefalakis and Giorgos Kapetanakis

Journal of Pure and Applied Algebra, 2019

DOI arXiv Bib

@article{garefalakiskapetanakis19a,
  author = {Garefalakis, Theodoulos and Kapetanakis, Giorgos},
  title = {On the existence of primitive completely normal bases of finite fields},
  journal = {Journal of Pure and Applied Algebra},
  volume = {223},
  number = {3},
  pages = {909--921},
  year = {2019},
  doi = {10.1016/j.jpaa.2018.05.005}
}

2017

Prescribing coefficients of invariant irreducible polynomials

Giorgos Kapetanakis

Journal of Number Theory, 2017

DOI Bib PDF

@article{kapetanakis17,
  author = {Kapetanakis, Giorgos},
  title = {Prescribing coefficients of invariant irreducible polynomials},
  journal = {Journal of Number Theory},
  volume = {180},
  pages = {615--628},
  year = {2017},
  doi = {10.1016/j.jnt.2017.05.003}
}

Enumerating permutation polynomials

Theodoulos Garefalakis and Giorgos Kapetanakis

Finite Fields and Their Applications, 2017

DOI Bib PDF

@article{garefalakiskapetanakis17,
  author = {Garefalakis, Theodoulos and Kapetanakis, Giorgos},
  title = {Enumerating permutation polynomials},
  journal = {Finite Fields and Their Applications},
  volume = {47},
  pages = {85--93},
  year = {2017},
  doi = {10.1016/j.ffa.2017.06.007}
}

2015

A note on the Hansen-Mullen conjecture for self-reciprocal irreducible polynomials

Theodoulos Garefalakis and Giorgos Kapetanakis

Finite Fields and Their Applications, 2015

DOI Bib PDF

@article{garefalakiskapetanakis15,
  author = {Garefalakis, Theodoulos and Kapetanakis, Giorgos},
  title = {A note on the Hansen-Mullen conjecture for self-reciprocal irreducible polynomials},
  journal = {Finite Fields and Their Applications},
  number = {35},
  pages = {61--63},
  year = {2015},
  doi = {10.1016/j.ffa.2015.03.005}
}

2014

Normal bases and primitive elements over finite fields

Giorgos Kapetanakis

Finite Fields and Their Applications, 2014

DOI Bib PDF

@article{kapetanakis14b,
  author = {Kapetanakis, Giorgos},
  title = {Normal bases and primitive elements over finite fields},
  journal = {Finite Fields and Their Applications},
  volume = {26},
  pages = {123--143},
  year = {2014},
  doi = {10.1016/j.ffa.2013.12.002}
}

An extension of the (strong) primitive normal basis theorem

Giorgos Kapetanakis

Applicable Algebra in Engineering, Communication and Computing, 2014

DOI Bib HTML PDF

@article{kapetanakis14a,
  author = {Kapetanakis, Giorgos},
  title = {An extension of the (strong) primitive normal basis theorem},
  journal = {Applicable Algebra in Engineering, Communication and Computing},
  volume = {25},
  number = {5},
  pages = {311--337},
  year = {2014},
  doi = {10.1007/s00200-014-0230-7}
}

2012

On the Hansen-Mullen conjecture for self-reciprocal irreducible polynomials

Theodoulos Garefalakis and Giorgos Kapetanakis

Finite Fields and Their Applications, 2012

DOI Bib PDF

@article{garefalakiskapetanakis12,
  author = {Garefalakis, Theodoulos and Kapetanakis, Giorgos},
  title = {On the Hansen-Mullen conjecture for self-reciprocal irreducible polynomials},
  journal = {Finite Fields and Their Applications},
  volume = {18},
  number = {4},
  pages = {832--841},
  year = {2012},
  doi = {10.1016/j.ffa.2012.03.001}
}

unpublished

2025

Translates of completely normal elements and the Morgan-Mullen conjecture

Theodoulos Garefalakis and Giorgos Kapetanakis

2025

arXiv Bib

@unpublished{garefalakiskapetanakis25,
  author = {Garefalakis, Theodoulos and Kapetanakis, Giorgos},
  title = {Translates of completely normal elements and the Morgan-Mullen conjecture},
  year = {2025}
}

2024

Existence of primitive normal pairs over finite fields with prescribed subtrace

Kaustav Chatterjee, Giorgos Kapetanakis, Hariom Sharma, and Shailesh Kumar Tiwari

2024

arXiv Bib

@unpublished{chatterjeekapetanakistiwarisharma24,
  author = {Chatterjee, Kaustav and Kapetanakis, Giorgos and Sharma, Hariom and Tiwari, Shailesh Kumar},
  title = {Existence of primitive normal pairs over finite fields with prescribed subtrace},
  year = {2024}
}

2023

An inductive proof of the Frobenius coin problem of two denominators

Giorgos Kapetanakis and Ioannis Rizos

2023

arXiv Bib

Primitive normal pairs of elements with one prescribed trace

Arpan Chandra Mazumder, Himangshu Hazarika, Dhiren Kumar Basnet, and Giorgos Kapetanakis

2023

arXiv Bib

@unpublished{mazumderhazarikabasnetkapetanakis23,
  author = {Mazumder, Arpan Chandra and Hazarika, Himangshu and Basnet, Dhiren Kumar and Kapetanakis, Giorgos},
  title = {Primitive normal pairs of elements with one prescribed trace},
  year = {2023}
}

theses

2014

Polynomials with special properties over finite fields

Giorgos Kapetanakis

Department of Mathematics and Applied Mathematics, University of Crete, Heraklion, Greece, 2014

Bib HTML PDF Slides

@phdthesis{kapetanakisphd,
  author = {Kapetanakis, Giorgos},
  title = {Polynomials with special properties over finite fields},
  school = {Department of Mathematics and Applied Mathematics, University of Crete},
  location = {Heraklion, Greece},
  year = {2014}
}

2008

The prime number theorem in function fields

Giorgos Kapetanakis

Department of Mathematics, University of Crete, Heraklion, Greece, 2008

in Greek

Bib PDF Slides

@mastersthesis{kapetanakismsc,
  note = {in Greek},
  author = {Kapetanakis, Giorgos},
  title = {The prime number theorem in function fields},
  school = {Department of Mathematics, University of Crete},
  location = {Heraklion, Greece},
  year = {2008}
}

talks

2025

Normal and primitive normal elements with prescribed traces in intermediate extensions of finite fields

30th Conference on Applications of Computer Algebra (ACA 2025), Heraklion, Greece, Jul 2025

invited Slides Website
An estimate for incomplete mixed character sums and applications

10th Greek Algebra and Number Theory Conference, Heraklion, Greece, May 2025

invited Slides Website

2023

The existence of Fq-primitive points on curves using freeness

1st Greek Number Theory Meeting, Athens, Greece, Dec 2023

invited Slides Website
The line and the translate properties for r-primitive elements

15th International Conference on Finite Fields and Their Applications (Fq15), Paris, France, Jun 2023

Slides Website
The line and the translate properties for r-primitive elements

9th Greek Algebra and Number Theory Conference, Thessaloniki, Greece, May 2023

invited Slides Website
Towards the primitive completely normal basis theorem

Greek Algebra & Number Theory Seminar (GANT), Apr 2023

invited Slides Website

2021

The existence of Fq-primitive points on curves using freeness

Carleton Finite Fields eSeminar, Dec 2021

invited Slides Website
The existence of Fq-primitive points on curves using freeness

Post-graduate program workshop, Department of Mathematics, University of the Aegean, Karlovasi, Greece, Nov 2021

invited Slides Website
Towards the primitive completely normal basis theorem

Department of Mathematics and Applied Mathematics, University of Crete, Heraklion, Greece, May 2021

invited Slides Website

2019

The line and the translate problem for r-primitive elements

FENS, Sabanci University, Istanbul, Turkey, Apr 2019

invited Website

2018

(Almost) normal and (almost) primitive elements of finite fields

Department of Mathematics and Applied Mathematics, University of Crete, Heraklion, Greece, Nov 2018

invited Website
On the existence of primitive completely normal bases of finite fields

First Congress of Greek Mathematicians, Athens, Greece, Jun 2018

Slides Website
Variations of the primitive normal basis theorem

Antalya Algebra Days XX, Sirince, Turkey, May 2018

Slides Website

2017

Prescribing coefficients of invariant irreducible polynomials

FENS, Sabanci University, Istanbul, Turkey, Nov 2017

invited Website
Prescribing coefficients of invariant irreducible polynomials

Department of Mathematics, Bogazici University, Istanbul, Turkey, Nov 2017

invited Slides Website
On a conjecture of Morgan and Mullen

13th International Conference on Finite Fields and their Applications (Fq13), Gaeta, Italy, Jun 2017

Slides Website
Prescribing coefficients of invariant irreducible polynomials

Antalya Algebra Days XIX, Sirince, Turkey, May 2017

Slides Website
On a Conjecture of Morgan and Mullen

Department of Mathematics, Mimar Sinan Fine Arts University, Istanbul, Turkey, May 2017

Slides Website
On a Conjecture of Morgan and Mullen

Department of Mathematics, Bilkent University, Ankara, Turkey, Apr 2017

Slides Website

2016

Details of the proof of the Hansen-Mullen conjecture for self-reciprocal polynomials

FENS, Sabanci University, Istanbul, Turkey, Oct 2016

Website
The Hansen-Mullen conjecture for self-reciprocal polynomials

FENS, Sabanci University, Istanbul, Turkey, Oct 2016

Slides Website
Polynomials with Special Properties over Finite Fields

LabSEC, Federal University of Santa Catarina, Florianopolis, SC, Brazil, Feb 2016

Slides Website

2013

Normal Bases and Primitive Elements over Finite Fields

11th International Conference on Finite Fields and their Applications (Fq11), Magdeburg, Germany, Jul 2013

Slides

2012

An Extension of the Strong Primitive Normal Basis Theorem

RICAM-Workshop on Finite Fields and Their Applications: Character Sums and Polynomials, Strobl, Austria, Sep 2012

Slides Website

2011

On the Hansen-Mullen Conjecture for Self-Reciprocal Irreducible Polynomials

10th International Conference on Finite Fields and their Applications (Fq10), Ghent, Belgium, Jul 2011

Slides Website