Publication is planned for June 2004 | Hardback
| 400 pages |
ISBN: 0-521-83659-X
The seminal formula of Gross and Zagier relating
heights of
Heegner points to derivatives of the associated
Rankin L-series
has led to many generalisations and extensions
in a variety of
different directions, spawing a fertile area
of study that
remains active to this day. This volume,
based on a workshop on
Special Values of Rankin L-series held at
the MSRI in December
2001, is a collection of thirteen articles
written by many of the
leading contributors in the field, having
the Gross-Zagier
formula and its avatars as a common unifying
theme. It serves as
a valuable reference for mathematicians wishing
to become further
acquainted with the theory of complex multipication,
automorphic
forms, the Rankin-Selberg method, arithmetic
intersection theory,
Iwasawa theory, and other topics related
to the Gross-Zagier
formula.
Contributors
Bryan Birch, Benedict Gross, Dorian goldfeld,
Brian Conrad,
Vinayak Vatsal, Shouwu Zhang, Stephen Kudla,
Tonghai Yang, Henri
Darmon, Adrian Lovita, Massimo Bertonlini,
Peter Green
Publication is planned for August 2004 |
Hardback | 170 pages
3 line diagrams | ISBN: 0-521-83920-3
Here the authors formulate and explore a
new axiom of set theory,
CPA, the Covering Property Axiom. CPA is
consistent with the
usual ZFC axioms, indeed it is true in the
iterated Sacks model
and actually captures the combinatorial core
of this model. A
plethora of results known to be true in the
Sacks model easily
follow from CPA. Replacing iterated forcing
arguments with
deductions from CPA simplifies proofs, provides
deeper insight,
and leads to new results. One may say that
CPA is similar in
nature to Martin's axiom, as both capture
the essence of the
models of ZFC in which they hold. The exposition
is a self
contained and there are natural applications
to real analysis and
topology. Researchers that use set theory
in their work will find
much of interest in this book.
Contents
1. Axiom CPAcube and its consequesnces: properties
(A)-(E); 2.
Games and axiom CPAgame/cube; 3. Prisms and
axioms CPAgame/prism
and CPAprism; 4. CPAprism and coverings with
smooth functions; 5.
Applications of CPAgame/prism; 6. CPA and
properties (F*) and (G);
7. CPA in the Sacks model.
September 2004 | Paperback | 132 pages 58
line diagrams 5
tables 168 exercises | ISBN: 0-521-60090-1
September 2004 | Hardback | 132 pages 58
line diagrams 5 tables
168 exercises | ISBN: 0-521-84118-6
The theory of integer partitions is a subject
of enduring
interest. A major research area in its own
right, it has found
numerous applications, and celebrated results
such as the Rogers-Ramanujan
identities make it a topic filled with the
true romance of
mathematics. The aim in this introductory
textbook is to provide
an accessible and wide ranging introduction
to partitions,
without requiring anything more of the reader
than some
familiarity with polynomials and infinite
series. Many exercises
are included, together with some solutions
and helpful hints. The
book has a short introduction followed by
an initial chapter
introducing Euler's famous theorem on partitions
with odd parts
and partitions with distinct parts. This
is followed by chapters
titled: Ferrers Graphs, The Rogers-Ramanujan
Identities,
Generating Functions, Formulas for Partition
Functions, Gaussian
Polynomials, Durfee Squares, Euler Refined,
Plane Partitions,
Growing Ferrers Boards, and Musings.
Contents
1. Introduction; 2. Euler and beyond; 3.
Ferrers graphs; 4. The
Rogers-Ramanujan identities; 5. Generating
functions; 6. Formulas
for partition functions; 7. Gaussian polynomials;
8. Durfee
squares; 9. Euler refined; 10. Plane partitions;
11. Growing
Ferrers board; 12. Musings; A. Infinite aeries
and products; B.
References; C. Solutions and hints.
Publication is planned for November 2004
| Paperback | ISBN: 0-521-60372-2
Publication is planned for November 2004
| Hardback | ISBN: 0-521-84283-2
This is a short course on Banach space theory
with special
emphasis on certain aspects of the classical
theory. In
particular, the course focuses on three major
topics: The
elementary theory of Schauder bases, an introduction
to Lp
spaces, and an introduction to C(K) spaces.
While these topics
can be traced back to Banach himself, our
primary interest is in
the postwar renaissance of Banach space theory
brought about by
James, Lindenstrauss, Mazur, Namioka, Pelczynski,
and others.
Their elegant and insightful results are
useful in many
contemporary research endeavors and deserve
greater publicity. By
way of prerequisites, the reader will need
an elementary
understanding of functional analysis and
at least a passing
familiarity with abstract measure theory.
An introductory course
in topology would also be helpful, however,
the text includes a
brief appendix on the topology needed for
the course.
Publication is planned for November 2004
| Paperback | 200
pages | ISBN: 0-521-54499-8
Publication is planned for November 2004
| Hardback | 200 pages |
ISBN: 0-521-83650-6
Combining a concrete perspective with an
exploration-based
approach, Exploratory Galois Theory develops
Galois theory at an
entirely undergraduate level. The text grounds
the presentation
in the concept of algebraic numbers with
complex approximations
and assumes of its readers only a first course
in abstract
algebra. The author organizes the theory
around natural questions
about algebraic numbers, and exercises with
hints and proof
sketches encourage students' participation
in the development.
For readers with Maple or Mathematica, the
text introduces tools
for hands-on experimentation with finite
extensions of the
rational numbers, enabling a familiarity
never before available
to students of the subject. Exploratory Galois
Theory includes
classical applications, from ruler-and-compass
constructions to
solvability by radicals, and also outlines
the generalization
from subfields of the complex numbers to
arbitrary fields. The
text is appropriate for traditional lecture
courses, for
seminars, or for self-paced independent study
by undergraduates
and graduate students.
Contents
1. Preliminaries; 2. Algebraic numbers, field
extension, and
minimal polynomials; 3. Working with algebraic
numbers, field
extension, and minimal polynomial; 4. Multiply-generated
fields;
5. The galois correspondence; 6. Some classical
topics;
Historical note.