LIST OF PUBLICATIONS


PAPERS:

  1. with Min Sha, Igor E. Shparlinski and Cameron L. Stewart: On multiplicatively dependent vectors of algebraic numbers. Trans. Amer. Math. Soc. 370 (2018), no. 9, 6221-6244.*

  2. with Kalyan Chakraborty and Jorge Jimènez Urroz: Pairs of integers which are mutually squares. Sci. China Math. 60 (2017), no. 9, 1633-1646.*

  3. with M. Anwar: On simultaneous primitive roots. Acta Arith. 180 (2017), no. 1, 35-43. *

  4. with A. Susa: An analogue to Artin's conjecture for multiplicative subgroups of the rationals. Arch. Math. 101 (2013), 319-330 *

  5. Divisibility of reduction in groups of rational numbers Math. Comp. 84 (2015), 385-407 *

  6. On the exponents of the group of points of an Elliptic curve over a finite field. Proc. Amer. Math. Soc. 139 No. 7 (2011) 2337-2341. *

  7. with W. Banks and I. Shparlinski: Possible Group Structures of Elliptic Curves over Finite Fields. Experimental Mathematics 21, Issue 1, March 2012, pages 11-25. *

  8. with Étienne Fouvry, F. Luca and I. Shparlinski: Counting dihedral and quaternionic extensions. Trans. Amer. Math. Soc. 363 No. 6 (2011) 3233-3253. *

  9. with S. D. Adhikari, R. Balasubramanian and P. Rath: Some zero-sum constants with weights. Proceedings of Indian Academy of Sciences. 118, No. 2, (2008), 183-188. *

  10. with F. Luca: Composite positive integers with an average prime factor. Acta Arithmetica 129 (2007), 197-201 *

  11. with Arto Lepistö and Kalle Saari: Transposition Invariant Words. Theoretical Computer Science 380, Issue 3 (June 2007) 377-387, Combinatorics on words. *

  12. with A. Glibichuk and F. Luca: On the equation t(l(n))=w(n)+k. Michigan Mathamatical Journal 55, Issue 3 (2007), 671-692. *

  13. with A. Susa: On a problem of Schinzel and Wójcik involving equalities between multiplicative orders. Math. Proc. Cambridge Philos. Soc. 146.2 (2009), 303-319. *

  14. with W. Banks, K. Ford, F. Luca and I. Shparlinski: Values of the Euler Function in Various Sequences. Monats. Math. 146 (2005), 1-19. *

  15. with W. Banks, J. B. Friedlander, F. Luca and I. Shparlinski: Coincidences in the Values of the Euler and Carmichael Functions. Acta Arithmetica 122.3 (2006), 207-234. *

  16. with Alf van der Poorten: Pseudo-Elliptic Integrals, Units and Torsion. J. Aust. Math. Soc. 79 (2005), 335-347. *

  17. A survey on k-power freeness. Proceeding of the Conference in Analytic Number Theory in Honor of Prof. Subbarao at I.M.Sc. Chennai, January 2003. Number theory, 71--88, Ramanujan Math. Soc. Lect. Notes Ser. 1, Ramanujan Math. Soc., Mysore, 2005. *

  18. with W. Banks: Powerfree Values of the Euler Function. J. Num. Theory 120 (2006) 326-348. *

  19. with F. Luca: Members of binary recurrences on lines of the Pascal triangle. Publ. Math. Debrecen 67 1-2 (2005) 103-113. *

  20. with S. das Adhikari, Y. G. Chen, J. B. Friedlander, S. Konyagin: Contributions to zero-sum problems. Discrete Math 306 (2006), 1-10. *

  21. with S. Konyagin: Enumerating permutation polynomials over finite fields by degree II. Finite Fields and their Applications 12 (2006) 26-37. *

  22. Squarefree Values of the Order Function. New York Journal of Mathematics 9 (2003), 331-344. *

  23. with F. Saidak and I. Shparlinski: Squarefree Values of the Carmichael Function. J. Num. Theory 103 (2003) 122-131. *

  24. with D. Cosentino: Fast computation of k-dimensional residues and an application to probabilistic encryption. *

  25. with C. David: Average Frobenius Distribution for inerts in Q(i). Journal of the Ramanujan Mathematical Society 19 (2004, no 3), 1-21. *

  26. with C. Malvenuto: Enumerating Permutation Polynomials II: k-cycles with minimal degree. Finite Fields and their Applications 10 (2004) 62-76. *

  27. with S. das Adhikari: On the visibility problem in the function field case. C. R. Math. Acad. Sci. Soc. R. Can. 24 (2002), no. 3, 109-116. *

  28. with S. Konyagin: Enumerating Permutation Polynomials over finite fields by degree. Finite Fields and their Applications 8 (2002) 548-553. *

  29. with C. Malvenuto: Enumerating Permutation Polynomials I: Permutations with non maximal degree. Finite Fields and their Applications 8 (2002) 531-547. * - corrigendum ibid. 13 1 (2007) 171-174. *

  30. with B. Mans and I. Shparlinski: On the spectral Adams property for circulant graphs. Discrete Math. 254 (2002) 309-329. *

  31. with E. Croot, D. E. Dobbs, J. B. Friedlander, A. J. Hetzel: Binary Egyptian Fractions. J. Num. Theory 84 (2000) 63-79. *

  32. with L. Cangelmi: On the r-rank Artin Conjecture II. J. Num. Theory 75 No.1 (1999) 120-132. *

  33. with C. David and H. Kisileveski: Galois representations with non surjective traces. Canad. J. Math. 51 No. 5 (1999) 936-951. *

  34. with C. David: Average Frobenius Distribution of Elliptic Curves. Internat. Math. Res. Notices 4 (1999) 165-183. *

  35. On Hooley's Theorem with weights. Rend. Sem. Mat. Polit. Univ. Torino 53 No. 4 (1995) 375-388. *

  36. with J. von zur Gathen: Density Estimates related to Gauss periods. Lam, Kwok-Yan (ed.) et al., Cryptography and computational number theory. Proceedings of the workshop, CCNT'99, Singapore, November 22-26, 1999. Basel: Birkhäuser. Prog. Comput. Sci. Appl. Log. 20, 33-41 (2001). *

  37. The r-rank Artin Conjecture. Math. Comp. 66 (1997) 853-868. *

  38. On the order of finitely generated subgroups of Q* and divisors of p-1. J. Num. Theory 57 No. 2 (1996) 207-222. *

  39. with I. Shparlinski: The Artin Conjecture for function fields. Finite Fields and their Applications 1 (1995) 399-404. *

  40. with H. Kisilevsky: On the exponent of the ideal class group of function fields. Acta Arithmetica LXXII No. 4 (1995) 311-321. *

  41. On minimal sets of generators for primitive roots. Bull. Canad. Math. Soc. 38 No. 4 (1995) 465-468. *

  42. On the exponent of the ideal class group of Q(Ö -d). Proc. Amer. Math. Soc. 123 No. 3 (1995) 663-671. *

  43. with H. E. Campbell, I. Hughes and P. Selik: On The ring of Invariants of F*2n. Comment. Math. Helvetici 66 (1991) 322-331. *
OTHER PUBLICATIONS:

    Editor: with F. Dramis, A. Gambacorta, R. Mignani and A. Trentalance Stato della Ricerca e sviluppi futuri: I primi dieci anni di attività della Facoltà M.F.N. di Roma Tre. Atti della Conferenza - Novembre 2001.

    Book: Note di crittografia a chiave pubblica.

    Book Review: with P. Mihailescu: Review of the book "Elliptic Curves in Cryptography" by I. Blake, G. Seroussi, N. Smart. Math. Comp. 2001. *

    with C. Malvenuto: On the Enumeration of Permutation Polynomials. Proc of Colloque LaCIM 2000 Combinatoire, Informatique et Applications Laboratoire de Combinatoire et d'Informatique Mathématique (LaCIM) Université du Québec à Montréal, 7 au 10 septembre 2000. *

    with B. Mans and I. Shparlinski: On Adams Conjecture for circulant graphs Hsu, Wen-Lian (ed.) et al., Computing and combinatorics. 4th annual international conference, COCOON '98, Taipei, Taiwan, ROC, August 12-14, 1998. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1449, 251-260 (1998). *

    Editor: with A. Perelli and C. Viola: Atti del Primo incontro Italiano di Teoria dei Numeri, Rend. Sem. Mat. Pol. Univ. Torino 53 No. 3-4 (1995).

    L'esponente del gruppo delle classi in campi di funzioni. Estratti Convegno Giornate di Geometria Algebrica ed argomenti Correlati III, L'Aquila 1995.

    PhD Thesis: Remarks on Artin Conjecture on Primitive Roots, McGill University, Montreal 1992. *

BEFORE NUMBER THEORY:

    with M. Fontana: Prime Spaces as Spectral Spaces. Annali di Matematica Pura ed Applicata (IV) 160 (1991) 331-345.

    Proceedings: Prime Spaces as Spectral Spaces, Convegno: "Alcuni aspetti della Teoria degli anelli commutativi" - Roma, 26 e 27 Maggio 1989.

    Tesi di Laurea: Sugli Spazi Spettrali, Nuovi Esempi ed Applicazioni Università La Sapienza, Roma, 1988.

November 2, 2010