Publications

Accepted

  1. A. Ghitza, T. Yamauchi: Automorphy of mod 2 Galois representations associated to certain genus 2 curves over totally real fields, Journal de Théorie des Nombres de Bordeaux 36, no. 2 (2024), 637-660.
  2. S. Anni, A. Ghitza, A. Medvedovsky: Elementary symmetric functions and deep power-sum congruences, Integers 24 (2024), Paper No. A46, 26 pp.
  3. A. Ghitza: Effective computation of Kurihara numbers, Appendix to Indivisibility of Kato's Euler systems and Kurihara numbers by Chan-Ho Kim, in Proceedings of the workshop Algebraic Number Theory and Related Topics 2018, RIMS Kôkyûroku Bessatsu B86 (2021), 63-86. Related code here.
  4. E. Eischen, M. Flander, A. Ghitza, E. Mantovan, A. McAndrew: Differential operators mod p: analytic continuation and consequences, Algebra and Number Theory 15, no. 6 (2021), 1469-1504.
  5. F. Calegari, S. Chidambaram, A. Ghitza: Some modular abelian surfaces, Mathematics of Computation 89, no. 321 (2020), 387-394.
  6. A. Ghitza: The Atkin-Lehner automorphism mod p geometrically, Appendix to Newforms mod p in squarefree level, with applications to Monsky's Hecke-stable filtration by S. V. Deo and A. Medvedovsky, Transactions of the American Mathematical Society Series B 6 (2019), 245-273.
  7. A. Ghitza: Differential operators on modular forms (mod p), Proceedings of the workshop Analytic and Arithmetic Theory of Automorphic Forms, RIMS Kôkyûroku No. 2100 (2019), 52-64.
  8. O. Colman, A. Ghitza, N. Ryan: Analytic evaluation of Hecke eigenvalues for Siegel modular forms of degree two, ANTS XIII, Proceedings of the 13th Algorithmic Number Theory Symposium, MSP Open Book Series 2, no. 1 (2019), 207-220. Related code here.
  9. P. Zimmermann, A. Casamayou, N. Cohen, G. Connan, T. Dumont, L. Fousse, F. Maltey, M. Meulien, M. Mezzarobba, C. Pernet, N. M. Thiéry, E. Bray, J. Cremona, M. Forets, A. Ghitza, H. Thomas: Computational Mathematics with SageMath, SIAM (2018), xiv+464 pages.
  10. S. Chow, A. Ghitza: Distinguishing newforms, International Journal of Number Theory 11, no. 3 (2015), 893-908. Related code here.
  11. A. Ghitza, R. Sayer: Hecke eigenvalues of Siegel modular forms of different weights, Journal of Number Theory 143, no. 10 (2014), 125-141.
  12. S. Chow, A. Ghitza: Distinguishing eigenforms modulo a prime ideal, Functiones et Approximatio Commentarii Mathematici 51, no. 2 (2014), 363-377.
  13. A. Ghitza, A. McAndrew: Experimental evidence for Maeda's conjecture on modular forms, Tbilisi Mathematical Journal 5, no. 2 (2012), 55-69.
  14. A. Ghitza, N. Ryan, D. Sulon: Computations of vector-valued Siegel modular forms, Journal of Number Theory 133, no. 11 (2013), 3921-3940.
  15. C. Citro, A. Ghitza: Computing level one Hecke eigensystems (mod p), LMS Journal of Computation and Mathematics 16 (2013), 246-270.
  16. C. Citro, A. Ghitza: Enumerating Galois representations in Sage, in K. Fukuda et al (Eds), Proceedings of the International Congress on Mathematical Software 2010, Lecture Notes in Computer Science 6327 (2010), 256-259.
  17. A. Ghitza: Distinguishing Hecke eigenforms, International Journal of Number Theory 7, no. 5 (2011), 1247-1253.
  18. A. Ghitza: All Siegel Hecke eigensystems (mod p) are cuspidal, Mathematical Research Letters 13, no. 5 (2006), 813-823.
  19. A. Ghitza: Upper bound on the number of systems of Hecke eigenvalues for Siegel modular forms (mod p), International Mathematics Research Notices, no. 55 (2004), 2983-2987.
  20. A. Ghitza: Hecke eigenvalues of Siegel modular forms (mod p) and of algebraic modular forms, Journal of Number Theory 106, no. 2 (2004), 345-384.

Submitted

Other

  1. I. Satake (translated by A. Ghitza): Translation of Ichiro Satake's paper Compactification des espaces quotients de Siegel II, Séminaire Henri Cartan 10, No. 2 (1957-1958). Translated pdf here.
  2. I. Satake (translated by A. Ghitza): Translation of Ichiro Satake's paper Compactification des espaces quotients de Siegel I, Séminaire Henri Cartan 10, No. 2 (1957-1958). Translated pdf here.
  3. J-P. Serre (translated by A. Ghitza): Translation of Jean-Pierre Serre's 1987 letter to Tate, later published as part of Two letters on quaternions and modular forms (mod p), Israel Journal of Mathematics 95, No. 1 (1996). Translated pdf here.
  4. J-P. Serre (translated by A. Ghitza): Translation of Jean-Pierre Serre's paper Sur les représentations modulaires de degré 2 de Gal(Qbar/Q), Duke Mathematical Journal 54, No. 1 (1987). Translated pdf here.
  5. J. Vélu (translated by A. Ghitza): Translation of Jacques Vélu's paper Isogénies entre courbes elliptiques, Comptes Rendus de l'Académie des Sciences de Paris, Série A 273, no. 4, 26 juillet 1971. Translated pdf here.
  6. A. Ghitza: Review of Lectures on NX(p) by Jean-Pierre Serre, Gazette of the Australian Mathematical Society 41, no. 5 (2014), 305-308.
  7. A. Ghitza: The abc conjecture, as easy as 1, 2, 3... or not, The Conversation 41, 26 November 2012.
  8. A. Ghitza: An elementary introduction to Siegel modular forms, survey, 12 pages, September 2004.

In preparation/limbo

  1. A. Ghitza, T. Yamauchi: The non-existence of some Galois representations of moderate degree in small characteristic, preprint (August 2025), 20 pages.
  2. A. Ghitza, M. Raum: HLinear - Exact Dense Linear Algebra in Haskell, 13 pages. Related code here and here.
  3. A. Ghitza, S. Mullane: Cohomological vanishing on Siegel modular varieties and applications to lifting Siegel modular forms, 18 pages.
  4. A. Ghitza, J.D. Lewis, K. Mansour, G. da Silva Jr.: The Hodge-D-Conjecture for a product of elliptic curves, 28 pages.
  5. D. Armendáriz, O. Colman, N. Coloma, A. Ghitza, N. Ryan, D. Terán: Analytic evaluation of Hecke eigenvalues for classical modular forms, 13 pages. Related code here.