Carlos Castano-Bernard

Research

My research is primarily concerned with the arithmetic of elliptic curves, Heegner objects and modular forms.

Publications:

• On Petersson's partition limit formula (with F. Luca), International Journal of Number Theory, 17 (2021), no. 6, pp. 1365-1378.
• On the parity of the index of ramified Heegner divisors, Boletín de la Sociedad Matemática Mexicana, 25 (2019), pp. 1-11
• A refinement of a conjecture of Gross, Kohnen, and Zagier, Contemporary Mathematics, 701 (2018), pp. 53-68
• Modular invariant of quantum tori (with T. Gendron), Proceedings of the London Mathematical Society, 109 (2014), no. 4, pp. 1014-1049
• An introduction to elliptic curve cryptography: an explicit approach, The Electronic Journal of Mathematics and Technology, 7 (2013) no. 4, pp. 245-263.
• A note on the rational points of X0+(N), Experimental Mathematics, 18 (2009), no. 2, pp. 129-135.
• Further properties of a function of Ogg and Ligozat, The Ramanujan Journal, 17 (2008), no. 1, pp. 107-121
• On the index of the Heegner subgroup of elliptic curves, TUCS General Publication, 46 (2007), pp. 23-35.

Facultad de Ciencias
Bernal Diaz del Castillo 340
28045 Colima
Mexico