Computing topological zeta functions of groups, algebras, and modules, I
Copyright policy )Computing topological zeta functions of groups, algebras, and modules, I
Building on our previous work (arXiv:1405.5711), we develop the first practical algorithm for computing topological zeta functions of nilpotent groups, non-associative algebras, and modules. While we previously depended upon non-degeneracy assumptions, the theory developed here allows us to overcome these restrictions in various interesting cases.
33 pages; sequel to arXiv:1405.5711
- Bielefeld University Germany
toric data, Subgroup theorems; subgroup growth, Group Theory (math.GR), Igusa-type zeta functions, Mathematics - Algebraic Geometry, FOS: Mathematics, Igusa zeta function, Number Theory (math.NT), Dirichlet series, Other Dirichlet series and zeta functions, Toric varieties, Newton polyhedra, Okounkov bodies, Algebraic Geometry (math.AG), subgroup growth, Mathematics - Number Theory, Arcs and motivic integration, nilpotent groups, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Asymptotic properties of groups, Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry), 11M41, 20F69, 14M25, General theory of nonassociative rings and algebras, topological zeta functions, Mathematics - Group Theory
toric data, Subgroup theorems; subgroup growth, Group Theory (math.GR), Igusa-type zeta functions, Mathematics - Algebraic Geometry, FOS: Mathematics, Igusa zeta function, Number Theory (math.NT), Dirichlet series, Other Dirichlet series and zeta functions, Toric varieties, Newton polyhedra, Okounkov bodies, Algebraic Geometry (math.AG), subgroup growth, Mathematics - Number Theory, Arcs and motivic integration, nilpotent groups, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Asymptotic properties of groups, Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry), 11M41, 20F69, 14M25, General theory of nonassociative rings and algebras, topological zeta functions, Mathematics - Group Theory
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