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Book DetailsContemporary MathematicsVolume: 566; 2012; 344 ppMSC: Primary 11; 14; 22; 32; 57
The volume contains the proceedings of the “Second International Workshop on Zeta Functions in Algebra and Geometry” held May 3–7, 2010 at the Universitat de les Illes Balears, Palma de Mallorca, Spain.
Zeta functions can be naturally attached to several mathematical objects, including fields, groups, and algebras. The conference focused on the following topics: arithmetic and geometric aspects of local, topological, and motivic zeta functions, Poincaré series of valuations, zeta functions of groups, rings, and representations, prehomogeneous vector spaces and their zeta functions, and height zeta functions.
This book is published in cooperation with Real Sociedád Matematica Española.ReadershipGraduate students and research mathematicians interested in zeta functions in number theory, geometry, and algebra.
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Table of Contents
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$L$-functions of varieties over finite fields and Artin $L$-functions
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Pilar Bayer — Computational aspects of Artin $L$-functions
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Anne Frühbis-Krüger and Shabnam Kadir — Zeta functions for families of Calabi–Yau $n$-folds with singularities
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Antonio Rojas-León — Estimates for exponential sums with a large automorphism group
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Height zeta functions and arithmetic
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Driss Essouabri — Height zeta functions on generalized projective toric varieties
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Yu. I. Manin — Combinatorial cubic surfaces and reconstruction theorems
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Sho Tanimoto and Yuri Tschinkel — Height zeta functions of equivariant compactifications of semi-direct products of algebraic groups
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Motivic zeta functions, Poincaré series, complex monodromy and knots
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Nero Budur — Singularity invariants related to Milnor fibers: survey
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Carlos Galindo and Francisco Monserrat — Finite families of plane valuations: value semigroup, graded algebra and Poincaré series
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E. Gorsky — $q,t$-Catalan numbers and knot homology
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Lars Halvard Halle and Johannes Nicaise — Motivic zeta functions for degenerations of abelian varieties and Calabi-Yau varieties
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András Némethi and Fernando Román — The lattice cohomology of $S^3_{-d}(K)$
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Zeta functions for groups and representations
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Nir Avni, Benjamin Klopsch, Uri Onn and Christopher Voll — Representation zeta functions of some compact $p$-adic analytic groups
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Aner Shalev — Applications of some zeta functions in group theory
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Additional Material
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
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The volume contains the proceedings of the “Second International Workshop on Zeta Functions in Algebra and Geometry” held May 3–7, 2010 at the Universitat de les Illes Balears, Palma de Mallorca, Spain.
Zeta functions can be naturally attached to several mathematical objects, including fields, groups, and algebras. The conference focused on the following topics: arithmetic and geometric aspects of local, topological, and motivic zeta functions, Poincaré series of valuations, zeta functions of groups, rings, and representations, prehomogeneous vector spaces and their zeta functions, and height zeta functions.
Graduate students and research mathematicians interested in zeta functions in number theory, geometry, and algebra.
-
$L$-functions of varieties over finite fields and Artin $L$-functions
-
Pilar Bayer — Computational aspects of Artin $L$-functions
-
Anne Frühbis-Krüger and Shabnam Kadir — Zeta functions for families of Calabi–Yau $n$-folds with singularities
-
Antonio Rojas-León — Estimates for exponential sums with a large automorphism group
-
Height zeta functions and arithmetic
-
Driss Essouabri — Height zeta functions on generalized projective toric varieties
-
Yu. I. Manin — Combinatorial cubic surfaces and reconstruction theorems
-
Sho Tanimoto and Yuri Tschinkel — Height zeta functions of equivariant compactifications of semi-direct products of algebraic groups
-
Motivic zeta functions, Poincaré series, complex monodromy and knots
-
Nero Budur — Singularity invariants related to Milnor fibers: survey
-
Carlos Galindo and Francisco Monserrat — Finite families of plane valuations: value semigroup, graded algebra and Poincaré series
-
E. Gorsky — $q,t$-Catalan numbers and knot homology
-
Lars Halvard Halle and Johannes Nicaise — Motivic zeta functions for degenerations of abelian varieties and Calabi-Yau varieties
-
András Némethi and Fernando Román — The lattice cohomology of $S^3_{-d}(K)$
-
Zeta functions for groups and representations
-
Nir Avni, Benjamin Klopsch, Uri Onn and Christopher Voll — Representation zeta functions of some compact $p$-adic analytic groups
-
Aner Shalev — Applications of some zeta functions in group theory
