论文信息 - Cubic Ramanujan graphs

Cubic Ramanujan graphs

A fimily of cubic Ramanujan graph is explicitly constructed. They are realized as Cayley graphs of a certain free group acting on the 3-regular tree; this group is obtained from a definite quaternion algebra that splits at the prime 2 and has a maximal order of class number 1.

Patrick Chiu | P. Chiu

[1] P. Sarnak. Some Applications of Modular Forms , 1990 .

[2] T. Apostol. Introduction to analytic number theory , 1976 .

[3] A. Lubotzky,et al. Hecke operators and distributing points on S2. II , 1987 .

[4] M. Eichler,et al. Quaternäre quadratische Formen und die Riemannsche Vermutung fÜr die Kongruenzzetafunktion , 1954 .

[5] Bruno Schoeneberg,et al. Elliptic Modular Functions , 1974 .

[6] A. Lubotzky,et al. Hecke operators and distributing points on the sphere I , 1986 .

[7] M. Eichler. Lectures on modular correspondences , 1955 .

[8] A. Ogg,et al. Modular forms and Dirichlet series , 1969 .

[9] R. Rankin. Modular Forms and Functions , 1977 .

[10] J. Igusa,et al. Fibre Systems of Jacobian Varieties: (III. Fibre Systems of Elliptic Curves) , 1959 .

[11] Martin Eichler,et al. The Basis Problem for Modular Forms and the Traces of the Hecke Operators , 1973 .

[12] M. Vignéras. Arithmétique des Algèbres de Quaternions , 1980 .