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Arithmetic and Geometry: Ten Years in Alpbach (AMS-202)

Gisbert Wüstholz and Clemens Fuchs (eds)

Published in print:
2019
Published Online:
May 2020
ISBN:
9780691193779
eISBN:
9780691197548
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691193779.001.0001
Subject:
Mathematics, Geometry / Topology

This book presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures—which were delivered in celebration of the ... More


Introduction

Gisbert Wüstholz and Clemens Fuchs (eds)

in Arithmetic and Geometry: Ten Years in Alpbach (AMS-202)

Published in print:
2019
Published Online:
May 2020
ISBN:
9780691193779
eISBN:
9780691197548
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691193779.003.0001
Subject:
Mathematics, Geometry / Topology

This introductory chapter provides an overview of the three topics discussed in this book: Shimura varieties, hyperelliptic continued fractions and generalized Jacobians, and Faltings heights and ... More


Hyperelliptic Continued Fractions and Generalized Jacobians: Minicourse Given by Umberto Zannier

Laura Capuano, Peter Jossen, Christina Karolus, and Francesco Veneziano

in Arithmetic and Geometry: Ten Years in Alpbach (AMS-202)

Published in print:
2019
Published Online:
May 2020
ISBN:
9780691193779
eISBN:
9780691197548
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691193779.003.0003
Subject:
Mathematics, Geometry / Topology

This chapter details Umberto Zannier's minicourse on hyperelliptic continued fractions and generalized Jacobians. It begins by presenting the Pell equation, which was studied by Indian, and later by ... More


An Introduction to Statistical Mechanics and Thermodynamics

Robert H. Swendsen

Published in print:
2019
Published Online:
February 2020
ISBN:
9780198853237
eISBN:
9780191887703
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198853237.001.0001
Subject:
Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

This is a textbook on statistical mechanics and thermodynamics. It begins with the molecular nature of matter and the fact that we want to describe systems containing many (1020) particles. The first ... More


Thermodynamic Identities

Robert H. Swendsen

in An Introduction to Statistical Mechanics and Thermodynamics

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199646944
eISBN:
9780191775123
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199646944.003.0014
Subject:
Physics, Condensed Matter Physics / Materials

Much of the power of thermodynamics is shown by its ability to relate apparently independent properties of thermodynamic systems through mathematical identities between partial derivatives. The ... More


Modular curves, modular forms, lattices, Galois representations

Bas Edixhoven

in Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691142012
eISBN:
9781400839001
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691142012.003.0002
Subject:
Mathematics, Number Theory

This chapter provides the necessary background concerning modular curves and modular forms. It covers modular curves, modular forms, lattices and modular forms, Galois representations attached to ... More


Morrey and Campanato vs. Hardy and John-Nirenberg Spaces

Ali Taheri

in Function Spaces and Partial Differential Equations: Volume 2: Contemporary Analysis

Published in print:
2015
Published Online:
September 2015
ISBN:
9780198733157
eISBN:
9780191797729
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198733157.003.0018
Subject:
Mathematics, Analysis

This chapter presents an analysis of decay rates of integral means of functions. It also provides an introduction of Morrey and Campanato spaces and their relation to Holder spaces. It also provides ... More


Thermodynamic Identities

Robert H. Swendsen

in An Introduction to Statistical Mechanics and Thermodynamics

Published in print:
2019
Published Online:
February 2020
ISBN:
9780198853237
eISBN:
9780191887703
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198853237.003.0014
Subject:
Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

Many of the calculations in thermodynamics concern the effects of small changes. To carry out such calculations, we often need to evaluate first and second partial derivatives of some thermodynamic ... More


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