Diofantove m-torke i eliptičke krivulje

Andrej Dujella:

Diofantove m-torke i eliptičke krivulje - Seminarske teme

1. Jake Diofantove m-torke (Stipe Marić, 27.4.2022.)

A. Dujella and V. Petričević, Strong Diophantine triples, Experiment. Math. 17 (2008), 83-89.
A. Dujella, I. Gusić, V. Petričević and P. Tadić, Strong Eulerian triples, Glas. Mat. Ser. III 53 (2018), 33-42.
A. Dujella, M. Paganin and M. Sadek, Strong rational Diophantine D(q)-triples, Indag. Math. (N.S.) 31 (2020), 505-511.

2. Eliptičke krivulje maksimalnog ranga (Dragana Kordić, 8.2.2023.)

J. Aguirre, A. Lozano-Robledo and J. C. Peral, Elliptic curves of maximal rank, Proceedings of the Segundas Jornadas de Teoria de Numeros, 1-28, Bibl. Rev. Mat. Iberoamericana, Madrid, 2008.
T. J. Kretschmer, Construction of elliptic curves with large rank, Math. Comp. 46 (1986), 627-635.
B. Mazur, Rational points of abelian varieties with values in towers of number fields, Invent. Math. 18 (1972), 183-266.

3. Mestreova uvjetna gornja ograda za rang

J. W. Bober, Conditionally bounding analytic ranks of elliptic curves, preprint, arXiv:1112.1503
J.-F. Mestre, Formules explicites et minorations de conducteurs de variétés algébriques, Compositio Math. 58 (1986), 209-232.
J.-F. Mestre and F. Sica, Curves with many points, Lecture notes, CICMA publications, 1997.
W. Stein, psage library

4. Mestreova polinomijalna metoda za netrivijalne torzijske grupe (David Tarandek, 7.12.2022.)

L. Kulesz and C. Stahlke, Elliptic curves of high rank with nontrivial torsion group over Q, Experiment. Math. 10 (2001), 475-480.
J. Aguirre, F. Castaneda and J. C. Peral, High rank elliptic curves with torsion group Z/(2Z), Math. Comp. 73 (2004), 323-331.
K. Nagao, Construction of high-rank elliptic curves with a nontrivial torsion point, Math. Comp. 66 (1997), 411-415.

5. Elkiesovi rezultati o krivuljama velikog ranga (Alen Andrašek)

N. D. Elkies, Three lectures on elliptic surfaces and curves of high rank, Lecture notes, Oberwolfach, 2007, arXiv:0709.2908
N. D. Elkies and Z. Klagsbrun, New rank records for elliptic curves having rational torsion, Proceedings of the Fourteenth Algorithmic Number Theory Symposium, Mathematical Sciences Publishers, Berkeley, 2020, pp. 233-250.
N. D. Elkies and N. F. Rogers, Elliptic curves x³ + y³ = k of high rank, Proceedings of ANTS-6 (D. Buell, ed.), Lecture Notes in Comput. Sci. 3076, Springer, 2004, 184-193.

6. Edwardsove krivulje i Diofantove m-torke (Valentina Pribanić, 4.5.2022.)

A. Dujella and M. Kazalicki, More on Diophantine sextuples, in Number Theory - Diophantine problems, uniform distribution and applications, Festschrift in honour of Robert F. Tichy's 60th birthday (C. Elsholtz, P. Grabner, Eds.), Springer-Verlag, Berlin, 2017, pp. 227-235.
M. Kazalicki and G. Dražić, Rational D(q)-quadruples, Indag. Math. (N.S.) 33 (2022), 440-449.
D. J. Bernstein, P. Birkner, M. Joye, T. Lange and Ch. Peters, Twisted Edwards curves, Progress in Cryptology - AFRICACRYPT 2008, Lecture Notes in Comput. Sci. 5023, Springer, 2008, pp. 389-405.

7. Eliptičke krivulje inducirane Diofantovim trojkama nad kvadratnim poljima (Domagoj Jelić, 25.5.2022.)

A. Dujella, M. Jukić Bokun and I. Soldo, On the torsion group of elliptic curves induced by Diophantine triples over quadratic fields, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 111 (2017), 1177-1185.
J. Aguirre, A. Dujella, M. Jukić Bokun and J. C. Peral, High rank elliptic curves with prescribed torsion group over quadratic fields, Period. Math. Hungar. 68 (2014), 222-230.
F. Najman, Some rank records for elliptic curves with prescribed torsion over quadratic fields, An. Stiint. Univ. "Ovidius" Constanta Ser. Mat. 22 (2014), 215-220.
A. Dujella, High rank elliptic curves with prescribed torsion over quadratic fields

8. Algoritam za injektivne specijalizacije i neke primjene

I. Gusić and P. Tadić, Injectivity of the specialization homomorphism of elliptic curves, J. Number Theory 148 (2015), 137-152.
A. Dujella, I. Gusić and P. Tadić, The rank and generators of Kihara's elliptic curve with torsion Z/4Z over Q(t), Proc. Japan Acad. Ser. A Math. Sci. 91 (2015), 105-109.
A. Dujella, J. C. Peral and P. Tadić, Elliptic curves with torsion group Z/6Z, Glas. Mat. Ser. III 51 (2016), 321-333.

9. Eliptičke krivulje inducirane racionalnim Diofantovim četvorkama

A. Dujella and G. Soydan, On elliptic curves induced by rational Diophantine quadruples, Proc. Japan Acad. Ser. A Math. Sci. 98 (2022), 1-6.
A. Dujella, Irregular Diophantine m-tuples and elliptic curves of high rank, Proc. Japan Acad. Ser. A Math. Sci. 76 (2000), 66-67.
M. Sadek, T. Yesin, Divisibility by 2 on quartic models of elliptic curves and rational Diophantine D(q)-quintuples, preprint, arXiv:2205.11415.

10. Torzijske grupe familija krivulja induciranih Diofantovim trojkama

M. Mikić, On the Mordell-Weil group of elliptic curves induced by families of Diophantine triples, Rocky Mountain J. Math. 45 (2015), 1565-1589.
F. Najman, Integer points on two families of elliptic curves, Publ. Math. Debrecen 75 (2009), 401-418.
A. Dujella and A. Pethő, Integer points on a family of elliptic curves, Publ. Math. Debrecen 56 (2000), 321-335.
K. Ono, Euler's concordant forms, Acta Arith. 78 (1996), 101-123.

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