Theory of Zeta-Functions of Root Systems

“The book is well structured … . This book can be a good tool for mathematicians interested in multivariable multiple zeta-functions since, together with new results presented and new methods introduced, it provides a necessary basis for the study of them or provide the links to suitable sources.” (Roma Kačinskaitė, zbMATH 1545.11002, 2024)

• ​Introduction.- Fundamentals of the theory of Lie algebras and root systems.- Definitions and examples.- Values at positive even integer points.- Convex polytopes and the rationality.- The recursive structure.- The meromorphic continuation.- Functional relations (I).- Functional relations (II).- Poincar´e polynomials and values at integer points .- The case of the exceptional algebra G2.- Applications to multiple zeta values (I).- Applications to multiple zeta values (II).- L-functions.-  Zeta-functions of Lie groups.- Lattice sums of hyperplane arrangements.- Miscellaneous results.