I am interested in all aspects of finite fields and their applications including: polynomials, normal bases, primitive elements, permutation polynomials, coding theory and cryptography.
Mathematical journal publications
S.D. Cohen, G. Kapetanakis and L. Reis. The existence of Fq-primitive points on curves using freeness. Comptes Rendus Math., 360(G6):641-652, 2022. [arXiv, DOI]
S.D. Cohen and G. Kapetanakis. The trace of primitive and 2-primitive elements in finite fields, revisited. Southeast Asian Bull. Math., to appear, 2022. [arXiv]
H. Hazarika, D.K. Basnet and G. Kapetanakis. On the existence of primitive normal elements of rational form over finite fields of even characteristic. Internat. J. Algebra Comput., 32(2):357-382, 2022. [arXiv, DOI]
S.D. Cohen and G. Kapetanakis. Finite field extensions with the line or translate property for r-primitive elements. J. Aust. Math. Soc., 111(3):313-319, 2021. [arXiv, DOI, Cambridge Core Share]
S.D. Cohen and G. Kapetanakis. The translate and line properties for 2-primitive elements in quadratic extensions. Int. J. Number Theory, 16(9):2029-2040, 2020. [arXiv, DOI]
S.D. Cohen and G. Kapetanakis. The trace of 2-primitive elements of finite fields. Acta Arith., 192(4):397-419, 2020. [arXiv, DOI]
T. Garefalakis and G. Kapetanakis. Further results on the Morgan-Mullen conjecture. Des. Codes Cryptogr., 87(11):2639-2654, 2019. [arXiv, DOI, ShareIt]
G. Kapetanakis. A Swan-like note for a family of binary pentanomials. Appl. Algebra Engrg. Comm. Comput., 30(5):361-372, 2019. [pdf, arXiv, DOI, ShareIt]
G. Kapetanakis and L. Reis. Variations of the primitive normal basis theorem. Des. Codes Cryptogr., 87(7):1459-1480, 2019. [pdf, arXiv, DOI]
T. Garefalakis and G. Kapetanakis. On the existence of primitive completely normal bases of finite fields. J. Pure Appl. Algebra, 223(3):909-921, 2019. [pdf, arXiv, DOI]
G. Kapetanakis. Prescribing coefficients of invariant irreducible polynomials. J. Number Theory, 180:615-628, 2017. [pdf, DOI]
T. Garefalakis and G. Kapetanakis. Enumerating permutation polynomials. Finite Fields Appl., 47:85-93, 2017. [pdf, DOI]
T. Garefalakis and G. Kapetanakis. A note on the Hansen-Mullen conjecture for self-reciprocal irreducible polynomials. Finite Fields Appl., 35:61-63, 2015. [pdf, DOI]
G. Kapetanakis. Normal bases and primitive elements over finite fields. Finite Fields Appl., 26:123-143, 2014. [pdf, DOI]
G. Kapetanakis. An extension of the (strong) primitive normal basis theorem. Appl. Algebra Engrg. Comm. Comput., 25(5):311-337, 2014. [pdf, DOI, ShareIt]
T. Garefalakis and G. Kapetanakis. On the Hansen-Mullen conjecture for self-reciprocal irreducible polynomials. Finite Fields Appl., 18(4):832-841, 2012. [pdf, DOI]
Other journal publications
G. Kapetanakis and I. Rizos. Teaching perspectives of the Frobenius coin problem of two denominators. Teach. Math., XXVI(2):57-67, 2023. [arXiv, DOI]
Unpublished papers
K. Chatterjee, G. Kapetanakis, S.K. Tiwari and H. Sharma. A primitive normal pair with prescribed subtrace. Submitted for publication, 2024.
G. Kapetanakis and I. Rizos. An inductive proof of the Frobenius coin problem of two denominators. Submitted for publication, 2023. [arXiv]
A.C. Mazumder, H. Hazarika, D.K. Basnet and G. Kapetanakis. Primitive normal pairs of elements with one prescribed trace. Submitted for publication, 2023. [arXiv]
Ενδιαφέρομαι για όλες τις πτυχές των πεπερασμένων σωμάτων και των εφαρμογών τους, όπως: πολυώνυμα, κανονικές βάσεις, πρωταρχικά στοιχεία, πολυώνυμα μετάθεσης, θεωρία κωδίκων και κρυπτογραφία.
Δημοσιευσεις σε επιστημονικα περιοδικα μαθηματικων
S.D. Cohen, G. Kapetanakis and L. Reis. The existence of Fq-primitive points on curves using freeness. Comptes Rendus Math., 360(G6):641-652, 2022. [arXiv, DOI]
S.D. Cohen and G. Kapetanakis. The trace of primitive and 2-primitive elements in finite fields, revisited. Southeast Asian Bull. Math., υπό δημοσίευση, 2022. [arXiv]
H. Hazarika, D.K. Basnet and G. Kapetanakis. On the existence of primitive normal elements of rational form over finite fields of even characteristic. Internat. J. Algebra Comput., 32(2):357-382, 2022. [arXiv, DOI]
S.D. Cohen and G. Kapetanakis. Finite field extensions with the line or translate property for r-primitive elements. J. Aust. Math. Soc., 111(3):313-319, 2021. [arXiv, DOI, Cambridge Core Share]
S.D. Cohen and G. Kapetanakis. The translate and line properties for 2-primitive elements in quadratic extensions. Int. J. Number Theory, 16(9):2029-2040, 2020. [arXiv, DOI]
S.D. Cohen and G. Kapetanakis. The trace of 2-primitive elements of finite fields. Acta Arith., 192(4):397-419, 2020. [arXiv, DOI]
T. Garefalakis and G. Kapetanakis. Further results on the Morgan-Mullen conjecture. Des. Codes Cryptogr., 87(11):2639-2654, 2019. [arXiv, DOI, ShareIt]
G. Kapetanakis. A Swan-like note for a family of binary pentanomials. Appl. Algebra Engrg. Comm. Comput., 30(5):361-372, 2019. [pdf, arXiv, DOI, ShareIt]
G. Kapetanakis and L. Reis. Variations of the primitive normal basis theorem. Des. Codes Cryptogr., 87(7):1459-1480, 2019. [pdf, arXiv, DOI]
T. Garefalakis and G. Kapetanakis. On the existence of primitive completely normal bases of finite fields. J. Pure Appl. Algebra, 223(3):909-921, 2019. [pdf, arXiv, DOI]
G. Kapetanakis. Prescribing coefficients of invariant irreducible polynomials. J. Number Theory, 180:615-628, 2017. [pdf, DOI]
T. Garefalakis and G. Kapetanakis. Enumerating permutation polynomials. Finite Fields Appl., 47:85-93, 2017. [pdf, DOI]
T. Garefalakis and G. Kapetanakis. A note on the Hansen-Mullen conjecture for self-reciprocal irreducible polynomials. Finite Fields Appl., 35:61-63, 2015. [pdf, DOI]
G. Kapetanakis. Normal bases and primitive elements over finite fields. Finite Fields Appl., 26:123-143, 2014. [pdf, DOI]
G. Kapetanakis. An extension of the (strong) primitive normal basis theorem. Appl. Algebra Engrg. Comm. Comput., 25(5):311-337, 2014. [pdf, DOI, ShareIt]
T. Garefalakis and G. Kapetanakis. On the Hansen-Mullen conjecture for self-reciprocal irreducible polynomials. Finite Fields Appl., 18(4):832-841, 2012. [pdf, DOI]
Δημοσιευσεις σε αλλα επιστημονικα περιοδικα
G. Kapetanakis and I. Rizos. Teaching perspectives of the Frobenius coin problem of two denominators. Teach. Math., XXVI(2):57-67, 2023. [arXiv, DOI]
Άρθρα υπό δημοσίευση
K. Chatterjee, G. Kapetanakis, S.K. Tiwari and H. Sharma. A primitive normal pair with prescribed subtrace. Έχει υποβληθεί προς δημοσίευση, 2024.
G. Kapetanakis and I. Rizos. An inductive proof of the Frobenius coin problem of two denominators. Έχει υποβληθεί προς δημοσίευση, 2023. [arXiv]
A.C. Mazumder, H. Hazarika, D.K. Basnet and G. Kapetanakis. Primitive normal pairs of elements with one prescribed trace. Έχει υποβληθεί προς δημοσίευση, 2023. [arXiv]
Νοέ 2021: Η ύπαρξη Fq-πρωταρχικών στοιχείων σε καμπύλες με χρήση ελεύθερων στοιχείων. Διημερίδα μαθηματικών στα πλαίσια του μεταπτυχιακού προγράμματος σπουδών "Σπουδές στα Μαθηματικά", Τμήμα Μαθηματικών, Πανεπιστήμιο Αιγαίιου, Καρλόβασι, Σάμος, Ελλάδα. (προσκεκλημένος) [διαφάνειες]
Οκτ 2016: Details of the proof of the Hansen-Mullen conjecture for self-reciprocal polynomials. FENS, Sabanci University, Κωνσταντινούπολη, Τουρκία. (σεμινάριο)