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. Takshak, G. Kapetanakis and R.K. Sharma. Fq-primitive points on varieties over finite fields. Finite Fields Appl., 103:102582, 2025. [arXiv, DOI]
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., 48(2): 161-184, 2024. [arXiv, pdf]
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
G. Kapetanakis and L. Reis. Normal points on Artin-Schreier curves over finite fields. Submitted for publication, 2024. [arXiv]
H. Hazarika, G. Kapetanakis and D.H. Basnet. Existence of Special Types Primitive Pairs in Finite Fields Avoiding Affine Hyperplanes. Submitted for publication, 2024. [arXiv]
K. Chatterjee, G. Kapetanakis, S.K. Tiwari and H. Sharma. Existence of primitive normal pairs over finite fields with prescribed subtrace. Submitted for publication, 2024. [arXiv]
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]
Feb 2016: Polynomials with Special Properties over Finite Fields. LabSEC, UFSC, Florianopolis, Brazil. [slides]
Jul 2013: Normal Bases and Primitive Elements over Finite Fields. 11th International Conference on Finite Fields and their Applications (Fq11), Magdeburg, Germany. [slides]
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. Takshak, G. Kapetanakis and R.K. Sharma. Fq-primitive points on varieties over finite fields. Finite Fields Appl., 103:102582, 2025. [arXiv, DOI]
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., 48(2): 161-184, 2024. [arXiv, pdf]
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
G. Kapetanakis and L. Reis. Normal points on Artin-Schreier curves over finite fields. Έχει υποβληθεί προς δημοσίευση, 2024. [arXiv]
H. Hazarika, G. Kapetanakis and D.H. Basnet. Existence of Special Types Primitive Pairs in Finite Fields Avoiding Affine Hyperplanes. Έχει υποβληθεί προς δημοσίευση, 2024. [arXiv]
K. Chatterjee, G. Kapetanakis, S.K. Tiwari and H. Sharma. Existence of primitive normal pairs over finite fields with prescribed subtrace. Έχει υποβληθεί προς δημοσίευση, 2024. [arXiv]
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. [https://arxiv.org/abs/2410.03836arXiv]
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)
Φεβ 2016: Polynomials with Special Properties over Finite Fields. LabSEC, UFSC, Φλοριανούπολη, Βραζιλία. [διαφάνειες]
Ιολ 2013: Normal Bases and Primitive Elements over Finite Fields. 11th International Conference on Finite Fields and their Applications (Fq11), Μαγδεβούργο, Γερμανία. [διαφάνειες]