Publications
Accepted
-
A. Ghitza,
T. Yamauchi:
Automorphy of mod 2 Galois representations associated to certain genus 2
curves over totally real fields, 17 pages, to appear in the
Journal de Théorie des Nombres de Bordeaux.
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S. Anni, A.
Ghitza,
A. Medvedovsky:
Elementary symmetric functions and deep power-sum congruences,
Integers
24
(2024),
Paper No. A46,
26 pp.
-
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.
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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.
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F. Calegari,
S. Chidambaram, A. Ghitza:
Some modular abelian surfaces,
Mathematics of Computation
89, no. 321
(2020), 387-394.
-
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.
-
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.
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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.
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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.
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S. Chow, A.
Ghitza:
Distinguishing newforms,
International Journal of Number Theory
11, no. 3
(2015), 893-908.
Related code here.
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A. Ghitza, R. Sayer:
Hecke eigenvalues of Siegel modular forms of different weights,
Journal of Number Theory
143, no. 10
(2014), 125-141.
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S. Chow, A.
Ghitza:
Distinguishing eigenforms modulo a prime ideal,
Functiones et Approximatio Commentarii Mathematici
51, no. 2
(2014), 363-377.
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A. Ghitza,
A. McAndrew:
Experimental evidence for Maeda's conjecture on modular forms,
Tbilisi Mathematical Journal
5, no. 2
(2012), 55-69.
-
A. Ghitza,
N. Ryan,
D. Sulon:
Computations of vector-valued Siegel modular forms,
Journal of Number Theory
133, no. 11
(2013), 3921-3940.
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C. Citro, A. Ghitza:
Computing level one Hecke eigensystems (mod p),
LMS Journal of Computation and Mathematics
16
(2013), 246-270.
-
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.
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A. Ghitza:
Distinguishing Hecke eigenforms,
International Journal of Number Theory
7, no. 5
(2011), 1247-1253.
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A. Ghitza:
All Siegel Hecke eigensystems (mod p) are cuspidal,
Mathematical Research Letters
13, no. 5
(2006), 813-823.
-
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.
-
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
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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.
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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.
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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.
-
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.
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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.
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A. Ghitza:
Review of Lectures on NX(p)
by
Jean-Pierre Serre,
Gazette of the Australian Mathematical Society
41, no. 5
(2014), 305-308.
-
A. Ghitza:
The abc conjecture, as easy as 1, 2, 3... or not,
The Conversation
41, 26 November 2012.
-
A. Ghitza:
An elementary introduction to Siegel modular forms, survey, 12 pages, September 2004.
In preparation/limbo
-
A. Ghitza,
M. Raum:
HLinear - Exact Dense Linear Algebra in Haskell, 13 pages.
Related code here
and
here.
-
A. Ghitza,
S. Mullane:
Cohomological vanishing on Siegel modular varieties and applications to
lifting Siegel modular forms, 18 pages.
-
A. Ghitza,
J.D. Lewis, K.
Mansour, G. da Silva Jr.:
The Hodge-D-Conjecture for a product of elliptic curves, 28 pages.
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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.