Giorgos N. Kapetanakis

Office 211, Building B

Department of Mathematics

University of Thessaly

Lamia, Greece

Welcome to my homepage. I am an Assistant Professor at the Department of Mathematics of the University of Thessaly. My research is focused on finite fields and their applications.

I obtained my BSc in Mathematics from the Department of Mathematics of the University of Athens. Then, I obtained my MSc in Pure Mathematics and my PhD in Mathematics from the Department of Mathematics and Applied Mathematics of the University of Crete.

After my studies, I held postdoc positions at the LabSEC of the Federal University of Santa Catarina and at the Algebra and Number Theory Group of Sabanci University and served as a Visiting Lecturer at the Department of Mathematics and Applied Mathematics of the University of Crete.

More details about my studies and my postdoctoral experience can be found at the cv section and, if you are a student, you can check the teaching section.

Last but not least, check at the Greek Algebra and Number Theory Seminar that I co-organize.

news

Oct 27, 2025	I will be giving a talk at the 3rd Greek Number Theory Meeting in Patras on 16-17 December 2025.
Sep 14, 2025	My office hours for the 2025-26 fall semester are Friday 12:00-13:00. However, you are strongly advised to communicate with me in advance.
Aug 28, 2025	About ACA 2025
Aug 26, 2025	After a long time, I finally migrated to a modern website, based on the al-folio theme. If you see anything that does not work or is missing, please let me know!

selected publications

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}
}

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}
}

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}
}

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}
}

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}
}