Filip Najman

Department of Mathematics
University of Zagreb
Bijenička cesta 30
10000 Zagreb
CROATIA

E-mail: fnajman@math.hr

Konzultacije (zimski semester 2016/2017): ponedjeljak 10-12

Soba: A305

 

 

Nastava 2016/2017:

Odabrana poglavlja teorije reprezentacija

 

Linkovi na neke kolegije koje sam držao:

Poslijediplomski - Eliptičke krivulje nad poljima algebarskih brojeva

 

 Publications:

1.      F. Najman, Compact representation of quadratic integers and integer points on some elliptic curves, Rocky Mountain J. Math. 40 (2010), 1979-2002.

2.      F. Najman, Integer points on two families of elliptic curves, Publ. Math. Debrecen 75 (2009), 401-418.

3.      F. Najman, Torsion of elliptic curves over cyclotomic quadratic fields, Math. J. Okayama Univ. 53 (2011), 75-82.

4.      F. Luca, F. Najman, On the largest prime factor of x^2-1, Math. Comp. 80 (2011), 429-435. Tables: odd solutions, even solutions

5.      F. Najman, The Diophantine equation x^4+-y^4=iz^2 in Gaussian integers, Amer. Math. Monthly 117 (2010), 637-641.

6.      F. Najman, Complete classification of torsion of elliptic curves over quadratic cyclotomic fields, J. Number Theory 130 (2010), 1964-1968

7.      F. Najman, Smooth values of some quadratic polynomials, Glasnik Mat. Ser III 45 (2010), 347-355. Values of x such that the polynomial is smooth: x^2+1, x^2+2, x^2+4, x^2-2, x^2-4. (For x^2+4 and x^2-4 only the odd values are listed).

8.      F. Najman, Large strings of consecutive smooth integers, Arch. Math. (Basel) 97 (2011), 319-324.

9.      S. Kamienny, F. Najman, Torsion groups of elliptic curves over quadratic fields, Acta. Arith. 152 (2012), 291-305.

10.      F. Najman, Torsion of elliptic curves over cubic fields, J. Number Theory, 132 (2012), 26-36.

11.      A. Dujella, F. Najman, Elliptic curves with large torsion and positive rank over number fields of small degree and ECM factorization, Period. Math. Hungar. 65 (2012), 193-203., special issue with papers from the “11th Central European Conference on Cryptography”.

12.      F. Najman, Exceptional elliptic curves over quartic fields, Int. J. Number Theory, 8 (2012), 1231-1246.

13.      F. Najman, On the number of elliptic curves with prescribed isogeny or torsion group over number fields of prime degree, Glasgow Math. J. 57 (2015), 465-473.

14.      J. Bosman, P. Bruin, A. Dujella, F. Najman,  Ranks of elliptic curves with prescribed torsion over number fields, Int. Math. Res. Not. IMRN 2014 (2014), 2885-2923.

15.      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., special issue with papers from the „Workshop on Algebraic and Analytic Number Theory and their Applicaitons“

16.      A. Dujella, F. Najman, N. Saradha, T. N. Shorey, Products of three factorials, Publ. Math. Debrecen 85 (2014) 123-130.

17.      P. Bruin, F. Najman, The growth of the rank of Abelian varieties upon extensions, Ramanujan J. 39 (2016), 259-269.

18.      F. Najman, Torsion of rational elliptic curves over cubic fields and sporadic points on X_1(n), Math. Res. Letters, 23 (2016) 245-272.

19.      F. Najman, The number of twists with large torsion of an elliptic curve, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 109 (2015), 535-547.

20.      P. Bruin, F. Najman, Hyperelliptic modular curves X_0(n) and isogenies of elliptic curves over quadratic fields, LMS J. Comput. Math. 18 (2015) 578-602.

21.      M. Mikić, F. Najman, On the number of n-isogenies of elliptic curves, Glasnik Mat. Ser III, 50 (2015) 333-348.

22.     E. Gonzalez-Jimenez, F. Najman, J. M. Tornero, Torsion of rational elliptic curves over cubic fields, Rocky Mountain J. Math, to appear.

23.     P. Bruin, F. Najman, A criterion to rule out torsion groups for elliptic curves over number fields, Research in Number Theory 2 (2016), 1-12.

24.     F. Najman, Isogenies of non-CM elliptic curves with rational j-invariants over number fields, submitted.

25.     H. B. Daniels, A. Lozano-Robledo, F. Najman, A. V. Sutherland, Torsion points on rational elliptic curves over the compositum of all cubic fields, Math. Comp. to appear.

26.     F. Najman, Tamagawa Numbers of elliptic curves with C_{13} torsion over quadratic fields, submitted.

27.     P. Bruin, F. Najman, Fields of definition of elliptic curves with prescribed torsion, submitted.

28.     E. Gonzalez-Jimenez, F. Najman, Growth of torsion groups of elliptic curves upon base change, preprint.