Concepedia

THE IHARA–SELBERG ZETA FUNCTION FOR PGL<sub>3</sub> AND HECKE OPERATORS

International Journal of Mathematics · 2006 · 10 citations · 6 references

Concepts

Spectral TheoryEngineeringRepresentation TheoryZeta FunctionsQuantum Field TheoryModular FormAnalytic Number TheoryAnalytic CombinatoricsAlgebraic CombinatoricsIhara FormulaTheta FunctionZeta Function

Abstract

A weak version of the Ihara formula is proved for zeta functions attached to quotients of the Bruhat–Tits building of PGL 3 . This formula expresses the zeta function in terms of Hecke-operators. It is the first step towards an arithmetical interpretation of the combinatorially defined zeta function.

References

6

THE IHARA-SELBERG ZETA FUNCTION OF A TREE LATTICE

Hyman Bass · International Journal of Mathematics · 1992 · 428 citations

Analytic Combinatorics, Analytic Number Theory, Theta Function +1

Zeta Functions of Finite Graphs and Coverings

H. Stärk, Audrey Terras · Advances in Mathematics · 1996 · 242 citations

Graph Theory, Algebraic Graph Theory, Zeta Functions +3

Zeta functions of finite graphs and coverings, III

Audrey Terras, H. Stärk · Advances in Mathematics · 2006 · 232 citations

Graph Theory, Algebraic Graph Theory, Zeta Functions +3

ON ZETA AND L-FUNCTIONS OF FINITE GRAPHS

International Journal of Mathematics · 1990 · 79 citations

Graph Theory, Algebraic Graph Theory, Topological Graph Theory +2

ARTIN TYPE L-FUNCTIONS AND THE DENSITY THEOREM FOR PRIME CYCLES ON FINITE GRAPHS

International Journal of Mathematics · 1992 · 52 citations

Geometric Graph Theory, Graph Theory, Algebraic Graph Theory +4