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Softcover ISBN:  9781470467791 
Product Code:  CONM/778 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9781470469764 
Product Code:  CONM/778.E 
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MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9781470467791 
eBook ISBN:  9781470469764 
Product Code:  CONM/778.B 
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Book DetailsContemporary MathematicsReal Sociedad Matemática EspañolaVolume: 778; 2022; 311 ppMSC: Primary 11; 14; 32; 82
This volume contains the proceedings of the 2019 Lluís A. Santaló Summer School on \(p\)Adic Analysis, Arithmetic and Singularities, which was held from June 24–28, 2019, at the Universidad Internacional Menéndez Pelayo, Santander, Spain.
The main purpose of the book is to present and analyze different incarnations of the local zeta functions and their multiple connections in mathematics and theoretical physics. Local zeta functions are ubiquitous objects in mathematics and theoretical physics. At the mathematical level, local zeta functions contain geometry and arithmetic information about the set of zeros defined by a finite number of polynomials. In terms of applications in theoretical physics, these functions play a central role in the regularization of Feynman amplitudes and KobaNielsentype string amplitudes, among other applications.
This volume provides a gentle introduction to a very active area of research that lies at the intersection of number theory, \(p\)adic analysis, algebraic geometry, singularity theory, and theoretical physics. Specifically, the book introduces \(p\)adic analysis, the theory of Archimedean, \(p\)adic, and motivic zeta functions, singularities of plane curves and their Poincaré series, among other similar topics. It also contains original contributions in the aforementioned areas written by renowned specialists.
This book is an important reference for students and experts who want to delve quickly into the area of local zeta functions and their many connections in mathematics and theoretical physics.
This book is published in cooperation with Real Sociedád Matematica Española.ReadershipGraduate students and research mathematicians interested in local zeta functions and their multiple connections in mathematics and theoretical physics.

Table of Contents

Surveys

Edwin LeónCardenal — Archimedean zeta functions and oscillatory integrals

Julio José MoyanoFernández — Generalized Poincaré series for plane curve singularities

Naud Potemans and Willem Veys — Introduction to $p$adic Igusa zeta functions

Juan ViuSos — An introduction to $p$adic and motivic integration, zeta functions and invariants of singularities

W. A. ZúñigaGalindo — $p$Adic analysis: A quick introduction

Articles

Enrique Artal Bartolo and Manuel González Villa — On maximal order poles of generalized topological zeta functions

José Ignacio CogolludoAgustín, Tamás László, Jorge MartínMorales and András Némethi — Local invariants of minimal generic curves on rational surfaces

János Nagy and András Némethi — Motivic Poincaré series of cusp surface singularities

Christopher D. Sinclair — NonArchimedean electrostatics


Additional Material

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This volume contains the proceedings of the 2019 Lluís A. Santaló Summer School on \(p\)Adic Analysis, Arithmetic and Singularities, which was held from June 24–28, 2019, at the Universidad Internacional Menéndez Pelayo, Santander, Spain.
The main purpose of the book is to present and analyze different incarnations of the local zeta functions and their multiple connections in mathematics and theoretical physics. Local zeta functions are ubiquitous objects in mathematics and theoretical physics. At the mathematical level, local zeta functions contain geometry and arithmetic information about the set of zeros defined by a finite number of polynomials. In terms of applications in theoretical physics, these functions play a central role in the regularization of Feynman amplitudes and KobaNielsentype string amplitudes, among other applications.
This volume provides a gentle introduction to a very active area of research that lies at the intersection of number theory, \(p\)adic analysis, algebraic geometry, singularity theory, and theoretical physics. Specifically, the book introduces \(p\)adic analysis, the theory of Archimedean, \(p\)adic, and motivic zeta functions, singularities of plane curves and their Poincaré series, among other similar topics. It also contains original contributions in the aforementioned areas written by renowned specialists.
This book is an important reference for students and experts who want to delve quickly into the area of local zeta functions and their many connections in mathematics and theoretical physics.
Graduate students and research mathematicians interested in local zeta functions and their multiple connections in mathematics and theoretical physics.

Surveys

Edwin LeónCardenal — Archimedean zeta functions and oscillatory integrals

Julio José MoyanoFernández — Generalized Poincaré series for plane curve singularities

Naud Potemans and Willem Veys — Introduction to $p$adic Igusa zeta functions

Juan ViuSos — An introduction to $p$adic and motivic integration, zeta functions and invariants of singularities

W. A. ZúñigaGalindo — $p$Adic analysis: A quick introduction

Articles

Enrique Artal Bartolo and Manuel González Villa — On maximal order poles of generalized topological zeta functions

José Ignacio CogolludoAgustín, Tamás László, Jorge MartínMorales and András Némethi — Local invariants of minimal generic curves on rational surfaces

János Nagy and András Némethi — Motivic Poincaré series of cusp surface singularities

Christopher D. Sinclair — NonArchimedean electrostatics