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A memorial conference for Leon Ehrenpreis was held at Temple
University, November 15-16, 2010. In the spirit of Ehrenpreis's
contribution to mathematics, the papers in this volume, written by
prominent mathematicians, represent the wide breadth of subjects
that Ehrenpreis traversed in his career, including partial
differential equations, combinatorics, number theory, complex
analysis and a bit of applied mathematics. With the exception of
one survey article, the papers in this volume are all new results
in the various fields in which Ehrenpreis worked . There are papers
in pure analysis, papers in number theory, papers in what may be
called applied mathematics such as population biology and parallel
refractors and papers in partial differential equations. The mature
mathematician will find new mathematics and the advanced graduate
student will find many new ideas to explore. A biographical sketch
of Leon Ehrenpreis by his daughter, a professional journalist,
enhances the memorial tribute and gives the reader a glimpse into
the life and career of a great mathematician.
A memorial conference for Leon Ehrenpreis was held at Temple
University, November 15-16, 2010. In the spirit of Ehrenpreis's
contribution to mathematics, the papers in this volume, written by
prominent mathematicians, represent the wide breadth of subjects
that Ehrenpreis traversed in his career, including partial
differential equations, combinatorics, number theory, complex
analysis and a bit of applied mathematics. With the exception of
one survey article, the papers in this volume are all new results
in the various fields in which Ehrenpreis worked . There are papers
in pure analysis, papers in number theory, papers in what may be
called applied mathematics such as population biology and parallel
refractors and papers in partial differential equations. The mature
mathematician will find new mathematics and the advanced graduate
student will find many new ideas to explore. A biographical sketch
of Leon Ehrenpreis by his daughter, a professional journalist,
enhances the memorial tribute and gives the reader a glimpse into
the life and career of a great mathematician."
The investigation of the relationships between compact Riemann
surfaces (al gebraic curves) and their associated complex tori
(Jacobi varieties) has long been basic to the study both of Riemann
surfaces and of complex tori. A Riemann surface is naturally
imbedded as an analytic submanifold in its associated torus; and
various spaces of linear equivalence elasses of divisors on the
surface (or equivalently spaces of analytic equivalence elasses of
complex line bundies over the surface), elassified according to the
dimensions of the associated linear series (or the dimensions of
the spaces of analytic cross-sections), are naturally realized as
analytic subvarieties of the associated torus. One of the most
fruitful of the elassical approaches to this investigation has been
by way of theta functions. The space of linear equivalence elasses
of positive divisors of order g -1 on a compact connected Riemann
surface M of genus g is realized by an irreducible (g
-1)-dimensional analytic subvariety, an irreducible hypersurface,
of the associated g-dimensional complex torus J(M); this hyper 1
surface W- r;;;, J(M) is the image of the natural mapping Mg-
-+J(M), and is g 1 1 birationally equivalent to the (g -1)-fold
symmetric product Mg- jSg-l of the Riemann surface M."
An essential undergraduate textbook on algebra, topology, and
calculus An Introduction to Analysis is an essential primer on
basic results in algebra, topology, and calculus for undergraduate
students considering advanced degrees in mathematics. Ideal for use
in a one-year course, this unique textbook also introduces students
to rigorous proofs and formal mathematical writing--skills they
need to excel. With a range of problems throughout, An Introduction
to Analysis treats n-dimensional calculus from the
beginning-differentiation, the Riemann integral, series, and
differential forms and Stokes's theorem-enabling students who are
serious about mathematics to progress quickly to more challenging
topics. The book discusses basic material on point set topology,
such as normed and metric spaces, topological spaces, compact sets,
and the Baire category theorem. It covers linear algebra as well,
including vector spaces, linear mappings, Jordan normal form,
bilinear mappings, and normal mappings. Proven in the classroom, An
Introduction to Analysis is the first textbook to bring these
topics together in one easy-to-use and comprehensive volume.
Provides a rigorous introduction to calculus in one and several
variables Introduces students to basic topology Covers topics in
linear algebra, including matrices, determinants, Jordan normal
form, and bilinear and normal mappings Discusses differential forms
and Stokes's theorem in n dimensions Also covers the Riemann
integral, integrability, improper integrals, and series expansions
The classical uniformization theorem for Riemann surfaces and its
recent extensions can be viewed as introducing special pseudogroup
structures, affine or projective structures, on Riemann surfaces.
In fact, the additional structures involved can be considered as
local forms of the uniformizations of Riemann surfaces. In this
study, Robert Gunning discusses the corresponding pseudogroup
structures on higher-dimensional complex manifolds, modeled on the
theory as developed for Riemann surfaces. Originally published in
1978. The Princeton Legacy Library uses the latest print-on-demand
technology to again make available previously out-of-print books
from the distinguished backlist of Princeton University Press.
These editions preserve the original texts of these important books
while presenting them in durable paperback and hardcover editions.
The goal of the Princeton Legacy Library is to vastly increase
access to the rich scholarly heritage found in the thousands of
books published by Princeton University Press since its founding in
1905.
The classical uniformization theorem for Riemann surfaces and its
recent extensions can be viewed as introducing special pseudogroup
structures, affine or projective structures, on Riemann surfaces.
In fact, the additional structures involved can be considered as
local forms of the uniformizations of Riemann surfaces. In this
study, Robert Gunning discusses the corresponding pseudogroup
structures on higher-dimensional complex manifolds, modeled on the
theory as developed for Riemann surfaces. Originally published in
1978. The Princeton Legacy Library uses the latest print-on-demand
technology to again make available previously out-of-print books
from the distinguished backlist of Princeton University Press.
These editions preserve the original texts of these important books
while presenting them in durable paperback and hardcover editions.
The goal of the Princeton Legacy Library is to vastly increase
access to the rich scholarly heritage found in the thousands of
books published by Princeton University Press since its founding in
1905.
This book is a sequel to Lectures on Complex Analytic Varieties:
The Local Paranwtrization Theorem (Mathematical Notes 10, 1970).
Its unifying theme is the study of local properties of finite
analytic mappings between complex analytic varieties; these
mappings are those in several dimensions that most closely resemble
general complex analytic mappings in one complex dimension. The
purpose of this volume is rather to clarify some algebraic aspects
of the local study of complex analytic varieties than merely to
examine finite analytic mappings for their own sake. Originally
published in 1970. The Princeton Legacy Library uses the latest
print-on-demand technology to again make available previously
out-of-print books from the distinguished backlist of Princeton
University Press. These editions preserve the original texts of
these important books while presenting them in durable paperback
and hardcover editions. The goal of the Princeton Legacy Library is
to vastly increase access to the rich scholarly heritage found in
the thousands of books published by Princeton University Press
since its founding in 1905.
A sequel to Lectures on Riemann Surfaces (Mathematical Notes,
1966), this volume continues the discussion of the dimensions of
spaces of holomorphic cross-sections of complex line bundles over
compact Riemann surfaces. Whereas the earlier treatment was limited
to results obtainable chiefly by one-dimensional methods, the more
detailed analysis presented here requires the use of various
properties of Jacobi varieties and of symmetric products of Riemann
surfaces, and so serves as a further introduction to these topics
as well. The first chapter consists of a rather explicit
description of a canonical basis for the Abelian differentials on a
marked Riemann surface, and of the description of the canonical
meromorphic differentials and the prime function of a marked
Riemann surface. Chapter 2 treats Jacobi varieties of compact
Riemann surfaces and various subvarieties that arise in determining
the dimensions of spaces of holomorphic cross-sections of complex
line bundles. In Chapter 3, the author discusses the relations
between Jacobi varieties and symmetric products of Riemann surfaces
relevant to the determination of dimensions of spaces of
holomorphic cross-sections of complex line bundles. The final
chapter derives Torelli's theorem following A. Weil, but in an
analytical context. Originally published in 1973. The Princeton
Legacy Library uses the latest print-on-demand technology to again
make available previously out-of-print books from the distinguished
backlist of Princeton University Press. These editions preserve the
original texts of these important books while presenting them in
durable paperback and hardcover editions. The goal of the Princeton
Legacy Library is to vastly increase access to the rich scholarly
heritage found in the thousands of books published by Princeton
University Press since its founding in 1905.
This book is a sequel to Lectures on Complex Analytic Varieties:
The Local Paranwtrization Theorem (Mathematical Notes 10, 1970).
Its unifying theme is the study of local properties of finite
analytic mappings between complex analytic varieties; these
mappings are those in several dimensions that most closely resemble
general complex analytic mappings in one complex dimension. The
purpose of this volume is rather to clarify some algebraic aspects
of the local study of complex analytic varieties than merely to
examine finite analytic mappings for their own sake. Originally
published in 1970. The Princeton Legacy Library uses the latest
print-on-demand technology to again make available previously
out-of-print books from the distinguished backlist of Princeton
University Press. These editions preserve the original texts of
these important books while presenting them in durable paperback
and hardcover editions. The goal of the Princeton Legacy Library is
to vastly increase access to the rich scholarly heritage found in
the thousands of books published by Princeton University Press
since its founding in 1905.
The present volume reflects both the diversity of Bochner's
pursuits in pure mathematics and the influence his example and
thought have had upon contemporary researchers. Originally
published in 1971. The Princeton Legacy Library uses the latest
print-on-demand technology to again make available previously
out-of-print books from the distinguished backlist of Princeton
University Press. These editions preserve the original texts of
these important books while presenting them in durable paperback
and hardcover editions. The goal of the Princeton Legacy Library is
to vastly increase access to the rich scholarly heritage found in
the thousands of books published by Princeton University Press
since its founding in 1905.
The present volume reflects both the diversity of Bochner's
pursuits in pure mathematics and the influence his example and
thought have had upon contemporary researchers. Originally
published in 1971. The Princeton Legacy Library uses the latest
print-on-demand technology to again make available previously
out-of-print books from the distinguished backlist of Princeton
University Press. These editions preserve the original texts of
these important books while presenting them in durable paperback
and hardcover editions. The goal of the Princeton Legacy Library is
to vastly increase access to the rich scholarly heritage found in
the thousands of books published by Princeton University Press
since its founding in 1905.
The description for this book, Lectures on Vector Bundles over
Riemann Surfaces. (MN-6), will be forthcoming.
New interest in modular forms of one complex variable has been
caused chiefly by the work of Selberg and of Eichler. But there has
been no introductory work covering the background of these
developments. H. C. Gunning's book surveys techniques and problems;
only the simpler cases are treated-modular forms of even weights
without multipliers, the principal congruence subgroups, and the
Hecke operators for the full modular group alone.
A sequel to Lectures on Riemann Surfaces (Mathematical Notes,
1966), this volume continues the discussion of the dimensions of
spaces of holomorphic cross-sections of complex line bundles over
compact Riemann surfaces. Whereas the earlier treatment was limited
to results obtainable chiefly by one-dimensional methods, the more
detailed analysis presented here requires the use of various
properties of Jacobi varieties and of symmetric products of Riemann
surfaces, and so serves as a further introduction to these topics
as well. The first chapter consists of a rather explicit
description of a canonical basis for the Abelian differentials on a
marked Riemann surface, and of the description of the canonical
meromorphic differentials and the prime function of a marked
Riemann surface. Chapter 2 treats Jacobi varieties of compact
Riemann surfaces and various subvarieties that arise in determining
the dimensions of spaces of holomorphic cross-sections of complex
line bundles. In Chapter 3, the author discusses the relations
between Jacobi varieties and symmetric products of Riemann surfaces
relevant to the determination of dimensions of spaces of
holomorphic cross-sections of complex line bundles. The final
chapter derives Torelli's theorem following A. Weil, but in an
analytical context. Originally published in 1973. The Princeton
Legacy Library uses the latest print-on-demand technology to again
make available previously out-of-print books from the distinguished
backlist of Princeton University Press. These editions preserve the
original texts of these important books while presenting them in
durable paperback and hardcover editions. The goal of the Princeton
Legacy Library is to vastly increase access to the rich scholarly
heritage found in the thousands of books published by Princeton
University Press since its founding in 1905.
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