research

journal articles

2025

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

   Himangshu Hazarika, Giorgos Kapetanakis, and Dhiren Kumar Basnet

   Appl. Algebra Engrg. Comm. Comput., 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 = {Appl. Algebra Engrg. Comm. Comput.},
     volume = {to appear},
     year = {2025},
     doi = {10.1007/s00200-025-00698-2}
   }

2. Normal points on Artin-Schreier curves over finite fields

   Giorgos Kapetanakis and Lucas Reis

   Comptes Rendus Math., 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 Math.},
     volume = {365},
     pages = {541--554},
     year = {2025},
     doi = {10.5802/crmath.740}
   }

3. Fq-primitive points on varieties over finite fields

   Soniya Takshak, Giorgos Kapetanakis, and Rajendra Kumar Sharma

   Finite Fields Appl., 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 Appl.},
     volume = {103},
     number = {102582},
     year = {2025},
     pages = {8pp.},
     doi = {10.1016/j.ffa.2025.102582}
   }

2024

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

   Stephen D. Cohen and Giorgos Kapetanakis

   Southeast Asian Bull. Math., 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 Bull. Math.},
     volume = {48},
     number = {2},
     pages = {161--184},
     year = {2024}
   }

2023

1. Teaching perspectives of the Frobenius coin problem of two denominators

   Giorgos Kapetanakis and Ioannis Rizos

   Teach. Math., 2023

   DOI arXiv Bib

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

2022

1. The existence of Fq-primitive points on curves using freeness

   Stephen D. Cohen, Giorgos Kapetanakis, and Lucas Reis

   Comptes Rendus Math., 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 Math.},
     volume = {360},
     pages = {641-652},
     year = {2022},
     doi = {10.5802/crmath.328}
   }

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

   Himangshu Hazarika, Dhiren Kumar Basnet, and Giorgos Kapetanakis

   Internat. J. Algebra Comput., 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 = {Internat. J. Algebra Comput.},
     volume = {32},
     number = {2},
     pages = {357--382},
     year = {2022},
     doi = {10.1142/S0218196722500187}
   }

2021

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

   Stephen D. Cohen and Giorgos Kapetanakis

   J. Aust. Math. Soc., 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 = {J. Aust. Math. Soc.},
     volume = {111},
     number = {3},
     pages = {313--319},
     year = {2021},
     doi = {10.1017/S1446788720000099}
   }

2020

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

   Stephen D. Cohen and Giorgos Kapetanakis

   Int. J. 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 = {Int. J. Number Theory},
     volume = {16},
     number = {9},
     pages = {2029--2040},
     year = {2020},
     doi = {10.1142/S1793042120501055}
   }

2. The trace of 2-primitive elements of finite fields

   Stephen D. Cohen and Giorgos Kapetanakis

   Acta Arith., 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 Arith.},
     volume = {192},
     number = {4},
     pages = {397-419},
     year = {2020},
     doi = {10.4064/aa190307-23-5}
   }

2019

1. Further results on the Morgan-Mullen conjecture

   Theodoulos Garefalakis and Giorgos Kapetanakis

   Des. Codes Cryptogr., 2019

   DOI arXiv Bib HTML

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

2. A Swan-like note for a family of binary pentanomials

   Giorgos Kapetanakis

   Appl. Algebra Engrg. Comm. Comput., 2019

   DOI arXiv Bib HTML

   @article{kapetanakis19,
     author = {Kapetanakis, Giorgos},
     title = {A Swan-like note for a family of binary pentanomials},
     journal = {Appl. Algebra Engrg. Comm. Comput.},
     volume = {30},
     number = {5},
     pages = {361--372},
     year = {2019},
     doi = {10.1007/s00200-018-0378-7}
   }

3. Variations of the primitive normal basis theorem

   Giorgos Kapetanakis and Lucas Reis

   Des. Codes Cryptogr., 2019

   DOI arXiv Bib

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

4. On the existence of primitive completely normal bases of finite fields

   Theodoulos Garefalakis and Giorgos Kapetanakis

   J. Pure Appl. 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 = {J. Pure Appl. Algebra},
     volume = {223},
     number = {3},
     pages = {909--921},
     year = {2019},
     doi = {10.1016/j.jpaa.2018.05.005}
   }

2017

1. Prescribing coefficients of invariant irreducible polynomials

   Giorgos Kapetanakis

   J. Number Theory, 2017

   DOI Bib PDF

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

2. Enumerating permutation polynomials

   Theodoulos Garefalakis and Giorgos Kapetanakis

   Finite Fields Appl., 2017

   DOI Bib PDF

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

2015

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

   Theodoulos Garefalakis and Giorgos Kapetanakis

   Finite Fields Appl., 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 Appl.},
     number = {35},
     pages = {61--63},
     year = {2015},
     doi = {10.1016/j.ffa.2015.03.005}
   }

2014

1. Normal bases and primitive elements over finite fields

   Giorgos Kapetanakis

   Finite Fields Appl., 2014

   DOI Bib PDF

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

2. An extension of the (strong) primitive normal basis theorem

   Giorgos Kapetanakis

   Appl. Algebra Engrg. Comm. Comput., 2014

   DOI Bib HTML PDF

   @article{kapetanakis14a,
     author = {Kapetanakis, Giorgos},
     title = {An extension of the (strong) primitive normal basis theorem},
     journal = {Appl. Algebra Engrg. Comm. Comput.},
     volume = {25},
     number = {5},
     pages = {311--337},
     year = {2014},
     doi = {10.1007/s00200-014-0230-7}
   }

2012

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

   Theodoulos Garefalakis and Giorgos Kapetanakis

   Finite Fields Appl., 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 Appl.},
     volume = {18},
     number = {4},
     pages = {832--841},
     year = {2012},
     doi = {10.1016/j.ffa.2012.03.001}
   }

unpublished

2025

1. 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

1. 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

1. An inductive proof of the Frobenius coin problem of two denominators

   Giorgos Kapetanakis and Ioannis Rizos

   2023

   arXiv Bib

   @unpublished{kapetanakisrizos23a,
     author = {Kapetanakis, Giorgos and Rizos, Ioannis},
     title = {An inductive proof of the Frobenius coin problem of two denominators},
     year = {2023}
   }

2. 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

1. 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

1. 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

1. 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
2. An estimate for incomplete mixed character sums and applications

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

   invited Slides Website

2023

1. The existence of Fq-primitive points on curves using freeness

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

   invited Slides Website
2. 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
3. The line and the translate properties for r-primitive elements

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

   invited Slides Website
4. Towards the primitive completely normal basis theorem

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

   invited Slides Website

2021

1. The existence of Fq-primitive points on curves using freeness

   Carleton Finite Fields eSeminar, Dec 2021

   invited Slides Website
2. 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
3. Towards the primitive completely normal basis theorem

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

   invited Slides Website

2019

1. The line and the translate problem for r-primitive elements

   FENS, Sabanci University, Istanbul, Turkey, Apr 2019

   invited Website

2018

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

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

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

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

   Slides Website
3. Variations of the primitive normal basis theorem

   Antalya Algebra Days XX, Sirince, Turkey, May 2018

   Slides Website

2017

1. Prescribing coefficients of invariant irreducible polynomials

   FENS, Sabanci University, Istanbul, Turkey, Nov 2017

   invited Website
2. Prescribing coefficients of invariant irreducible polynomials

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

   invited Slides Website
3. On a conjecture of Morgan and Mullen

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

   Slides Website
4. Prescribing coefficients of invariant irreducible polynomials

   Antalya Algebra Days XIX, Sirince, Turkey, May 2017

   Slides Website
5. On a Conjecture of Morgan and Mullen

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

   Slides Website
6. On a Conjecture of Morgan and Mullen

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

   Slides Website

2016

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

   FENS, Sabanci University, Istanbul, Turkey, Oct 2016

   Website
2. The Hansen-Mullen conjecture for self-reciprocal polynomials

   FENS, Sabanci University, Istanbul, Turkey, Oct 2016

   Slides Website
3. Polynomials with Special Properties over Finite Fields

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

   Slides Website

2013

1. Normal Bases and Primitive Elements over Finite Fields

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

   Slides

2012

1. 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

1. 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