GRAPH SPECTRA FOR FINITE UPPER HALF-PLANES OVER RINGS

被引：11

作者：

ANGEL, J ^{[1
]}

TRIMBLE, C ^{[1
]}

SHOOK, B ^{[1
]}

TERRAS, A ^{[1
]}

机构：

[1] UNIV CALIF SAN DIEGO, DEPT MATH, LA JOLLA, CA 92093 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 1995年 / 226卷

关键词：

D O I：

10.1016/0024-3795(95)00173-O

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Graphs attached for finite analogues of the Poincare upper half plane over rings Z/p(r)Z are introduced for p an odd prime. The spectra of these graphs for r = 2 are shown to be related to those for r = 1 which were studied earlier. In contrast to the case r = 1 , we find that the graphs are not Ramanujan graphs when r = 2 and p greater than or equal to 5. Histograms of the eigenvalues for r = 1 and 2 are also compared. The graphs over rings are of interest for connections with p-adic upper half planes as well as fundamental domains for congruence subgroups of the modular group SL(2, Z).

引用

页码：423 / 457

页数：35

共 10 条

[1]

Celniker N., 1993, CONT MATH, V143, P65

[2]

Chung F.R.K., 1989, J AM MATH SOC, V2, P187, DOI DOI 10.2307/1990973.MR965008

[3]

KATZ NM, 1993, J REINE ANGEW MATH, V438, P143

[4] RAMANUJAN GRAPHS [J].

LUBOTZKY, A ;

PHILLIPS, R ;

SARNAK, P .

COMBINATORICA, 1988, 8 (03) :261-277

[5]

Soto-Andrade, 1987, P S PURE MATH, V47, P305

[6]

Stark H. M., 1987, CAN MATH SOC C P, V7, P421

[7]

TERRAS A, 1991, DISCOURSES MATH APPL, P237

[8]

[No title captured]

[9]

[No title captured]

[10]

[No title captured]

← 1 →