A new generating function for calculating the Igusa local zeta function

DOI10.1016/j.aim.2016.09.003zbMath1396.11131arXiv1506.07869OpenAlexW2963346872MaRDI QIDQ329493

Raemeon A. Cowan, Daniel J. Katz, Lauren M. White

Publication date: 21 October 2016

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.07869

zbMATH Keywords

quadratic formgenerating function\(p\)-adic fieldIgusa local zeta function

Mathematics Subject Classification ID

Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Zeta functions and (L)-functions (11S40) Quadratic forms over local rings and fields (11E08)

Related Items (4)

Poincaré square series for the Weil representation ⋮ Vector-valued Eisenstein series of small weight ⋮ Overpartition $M2$-rank differences, class number relations, and vector-valued mock Eisenstein series ⋮ Poincaré and Eisenstein series for Jacobi forms of lattice index

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Exponential sums and polynomial congruences along \(p\)-adic submanifolds
• Functional equations for zeta functions of groups and rings
• Monodromy Jordan blocks, \(b\)-functions and poles of zeta functions for germs of plane curves
• Lectures on forms of higher degree. Notes by S. Raghavan
• Zeta functions of three-dimensional \(p\)-adic Lie algebras
• Local zeta function for nondegenerate homogeneous mappings
• Corrigendum to ``Decay of solutions of wave-type pseudo-differential equations over \(p\)-adic fields
• On the poles of a local zeta function for curves
• Local zeta functions and Euler characteristics
• Local zeta functions of general quadratic polynomials
• Newton polyhedra and Igusa's local zeta function
• Local zeta functions and fundamental solutions for pseudo-differential operators over \(p\)-adic fields
• The Igusa local zeta function associated with the singular cases of the determinant and the Pfaffian
• Lower bound for the poles of Igusa's \(p\)-adic zeta functions
• Sur la formule de Siegel dans la théorie des groupes classiques
• A canonical quadratic form for the ring of 2-adic integers
• Igusa's local zeta functions of semiquasihomogeneous polynomials
• Poles of a Two-Variable P-Adic Complex Power
• Local Zeta Functions Supported on Analytic Submanifolds and Newton Polyhedra
• Vanishing of principal value integrals on surfaces
• On the unramified spectrum of spherical varieties over p-adic fields
• On ‘maximal’ poles of zeta functions, roots ofb-functions, and monodromy Jordan blocks
• Point count divisibility for algebraic sets over ℤ/𝕡^{ℓ}ℤ and other finite principal rings
• On the Poles of Igusa's Local Zeta Function for Curves
• A Functional Equation of Igusa's Local Zeta Function
• Complex powers and asymptotic expansions. II.
• Poles of Igusa's local zeta function and monodromy
• Zeta Functions for Curves and Log Canonical Models
• Dirichlet series in two variables
• Pseudo-differential equations connected with p-adic forms and local zeta functions
• Complex powers and asymptotic expansions. I. Functions of certain types.
• Local zeta function for curves, non-degeneracy conditions and Newton polygons
• Local zeta functions and Newton polyhedra
• ON THE POLES OF IGUSA'S LOCAL ZETA FUNCTION FOR ALGEBRAIC SETS
• On the Holomorphy Conjecture for Igusa's Local Zeta Function
• Zeros of Polynomials over Finite Principal Ideal Rings
• Igusa-type functions associated to finite formed spaces and their functional equations
• Zeta functions for analytic mappings, log-principalization of ideals, and Newton polyhedra
• Analytic properties of zeta functions and subgroup growth

This page was built for publication: A new generating function for calculating the Igusa local zeta function