Alex Ghitza

Publications

Accepted

  1. 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 Kokyuroku Bessatsu B86 (2021), 63-86.
  2. 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
  3. F. Calegari, S. Chidambaram, A. Ghitza, Some modular abelian surfaces, Math. Comp. 89 (2020), 387-394.
  4. 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, Trans. Amer. Math. Soc. Ser. B 6 (2019), 245-273.
  5. A. Ghitza, Differential operators on modular forms (mod p), Proceedings of the workshop Analytic and Arithmetic Theory of Automorphic Forms, RIMS Kokyuroku No. 2100 (2019), 52-64.
  6. 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, Open Book Series 2, no. 1 (2019), 207-220.
  7. 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.
  8. S. Chow, A. Ghitza, Distinguishing newforms, Int. J. Number Theory 11, no. 3 (2015), 893-908.
  9. A. Ghitza, R. Sayer, Hecke eigenvalues of Siegel modular forms of different weights, J. Number Theory 143, no. 10 (2014), 125-141.
  10. S. Chow, A. Ghitza, Distinguishing eigenforms modulo a prime ideal, Funct. Approx. Comment. Math. 51, no. 2 (2014), 363-377.
  11. A. Ghitza, A. McAndrew, Experimental evidence for Maeda's conjecture on modular forms, Tbilisi Math. J. 5, no. 2 (2012), 55-69.
  12. A. Ghitza, N. Ryan, D. Sulon, Computations of vector-valued Siegel modular forms, J. Number Theory 133, no. 11 (2013), 3921-3940.
  13. C. Citro, A. Ghitza, Computing level one Hecke eigensystems (mod p), LMS J. Comput. Math. 16 (2013), 246-270.
  14. C. Citro, A. Ghitza, Enumerating Galois representations in Sage, K. Fukuda et al (Eds), Proceedings of the International Congress on Mathematical Software 2010, Lecture Notes in Computer Science 6327 (2010), 256-259.
  15. A. Ghitza, Distinguishing Hecke eigenforms, Int. J. Number Theory 7, no. 5 (2011), 1247-1253.
  16. A. Ghitza, All Siegel Hecke eigensystems (mod p) are cuspidal, Math. Res. Letters 13, no. 5 (2006), 813-823.
  17. A. Ghitza, Upper bound on the number of systems of Hecke eigenvalues for Siegel modular forms (mod p), IMRN, no. 55 (2004), 2983-2987.
  18. A. Ghitza, Hecke eigenvalues of Siegel modular forms (mod p) and of algebraic modular forms, J. Number Theory 106, no. 2 (2004), 345-384.

Submitted

  1. A. Ghitza, T. Yamauchi, Automorphy of mod 2 Galois representations associated to certain genus 2 curves over totally real fields, 17 pages.

In preparation

  1. S. Anni, A. Ghitza, A. Medvedovsky, Deep congruences + the Brauer-Nesbitt Theorem, 23 pages.
  2. A. Ghitza, J.D. Lewis, K. Mansour, G. da Silva Jr., The Hodge-D-Conjecture for a product of elliptic curves, 28 pages.
  3. D. Armendariz, O. Colman, N. Coloma, A. Ghitza, N. Ryan, D. Teran, Analytic evaluation of Hecke eigenvalues for classical modular forms, 13 pages.

Other

  1. 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, No. 95 (1996).
  2. J-P. Serre (translated by A. Ghitza), Translation of Jean-Pierre Serre's paper 'Sur les representations modulaires de degre 2 de Gal(Qbar/Q)', Duke Math. J. 54, No. 1 (1987).
  3. J. Velu (translated by A. Ghitza), Translation of Jacques Velu's paper 'Isogenies entre courbes elliptiques', Comptes Rendus de l'Academie des Sciences de Paris, Serie A 273, 26 juillet 1971.
  4. A. Ghitza, M. Raum, HLinear: Exact Dense Linear Algebra in Haskell, 12 pages.
  5. A. Ghitza, S. Mullane, Cohomological vanishing on Siegel modular varieties and applications to lifting Siegel modular forms, currently abandoned preprint
  6. A. Ghitza, Review of Lectures on $N_X(p)$ by Jean-Pierre Serre, Gazette Aust. Math. Soc 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.

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