Expected publication date is June 9, 2005
Description
Since the pioneering work of Euler, Dirichlet, and Riemann, the
analytic properties of L-functions have been used to study the
distribution of prime numbers. With the advent of the Langlands
Program, L-functions have assumed a greater role in the study of
the interplay between Diophantine questions about primes and
representation theoretic properties of Galois representations.
This book provides a complete introduction to the most
significant class of L-functions: the Artin-Hecke L-functions
associated to finite-dimensional representations of Weil groups
and to automorphic L-functions of principal type on the general
linear group. In addition to establishing functional equations,
growth estimates, and non-vanishing theorems, a thorough
presentation of the explicit formulas of Riemann type in the
context of Artin-Hecke and automorphic L-functions is also given.
The survey is aimed at mathematicians and graduate students who
want to learn about the modern analytic theory of L-functions and
their applications in number theory and in the theory of
automorphic representations. The requirements for a profitable
study of this monograph are a knowledge of basic number theory
and the rudiments of abstract harmonic analysis on locally
compact abelian groups.
Contents
Hecke L-functions
Artin-Hecke L-functions
Analytic properties of L-functions
The explicit formulas
Bounds on discriminants and conductors
Non-vanishing theorems
The local theory of root numbers: A survey
Bibliography
Index
Details:
Series: Mathematical Surveys and Monographs, Volume: 115
Publication Year: 2005
ISBN: 0-8218-3641-2
Paging: approximately 312 pp.
Binding: Hardcover
Expected publication date is June 2, 2005
Description
The study of the geometry of convex bodies based on information
about sections and projections of these bodies has important
applications in many areas of mathematics and science. In this
book, a new Fourier analysis approach is discussed. The idea is
to express certain geometric properties of bodies in terms of
Fourier analysis and to use harmonic analysis methods to solve
geometric problems.
One of the results discussed in the book is Ball's theorem,
establishing the exact upper bound for the (n-1)-dimensional
volume of hyperplane sections of the n-dimensional unit cube (it
is sqrt{2} for each ngeq 2). Another is the Busemann-Petty
problem: if K and L are two convex origin-symmetric n-dimensional
bodies and the (n-1)-dimensional volume of each central
hyperplane section of K is less than the (n-1)-dimensional volume
of the corresponding section of L, is it true that the n-dimensional
volume of K is less than the volume of L? (The answer is positive
for nle 4 and negative for n>4.)
The book is suitable for graduate students and researchers
interested in geometry, harmonic and functional analysis, and
probability. Prerequisites for reading this book include basic
real, complex, and functional analysis.
Contents
Introduction
Basic concepts
Volume and the Fourier transform
Intersection bodies
The Busemann-Petty problem
Intersection bodies and L_p-spaces
Extremal sections of ell_q-balls
Projections and the Fourier transform
Bibliography
Index
Details:
Series: Mathematical Surveys and Monographs, Volume: 116
Publication Year: 2005
ISBN: 0-8218-3787-7
Paging: 170 pp.
Binding: Hardcover
Expected publication date is June 3, 2005
Description
Robert Hartshorne's book, Residues and Duality (1966, Springer-Verlag),
introduced the notion of residual complexes and developed a
duality theory (Grothendieck duality) on the category of maps of
noetherian schemes.
The three articles in this volume constitute a reworking of the
main parts of the corresponding chapters in Hartshorne's 1966
book in greater generality using a somewhat different approach.
In particular, throughout this volume, the authors work with
arbitrary (quasi-coherent, torsion) Cousin complexes on formal
schemes, not only with residual complexes on ordinary schemes.
Additionally, their motivation is to help readers gain a better
understanding of the relation between local properties of
residues and global properties of the dualizing pseudofunctor.
The book is suitable for graduate students and researchers
working in algebraic geometry.
Contents
J. Lipman, S. Nayak, and P. Sastry -- Part 1. Pseudofunctorial
behavior of Cousin complexes on formal schemes
P. Sastry -- Part 2. Duality for Cousin complexes
S. Nayak -- Part 3. Pasting pseudofunctors
Index
Details:
Series: Contemporary Mathematics, Volume: 375
Publication Year: 2005
ISBN: 0-8218-3705-2
Paging: 276 pp.
Binding: Softcover
Expected publication date is July 9, 2005
Description
This book is written by award-winning author, Frank Morgan. It
offers a simple and sophisticated point of view, reflecting
Morgan's insightful teaching, lecturing, and writing style.
Intended for undergraduates studying real analysis, this book
builds the theory behind calculus directly from the basic
concepts of real numbers, limits, and open and closed sets in
mathbf{R}^n. It gives the three characterizations of continuity:
via epsilon-delta, sequences, and open sets. It gives the three
characterizations of compactness: as "closed and bounded,"
via sequences, and via open covers. Topics include Fourier
series, the Gamma function, metric spaces, and Ascoli's Theorem.
This concise text not only provides efficient proofs, but also
shows students how to derive them. The excellent exercises are
accompanied at the back of the book by select solutions. Ideally
suited as an undergraduate textbook, this complete book on real
analysis will fit comfortably into one semester.
Frank Morgan received the first national Haimo teaching award
from the Mathematical Association of America. He has also
garnered top teaching awards from Rice University (Houston, TX)
and MIT (Cambridge, MA).
Contents
Part I: Real numbers and limits
Numbers and logic
Infinity
Sequences
Functions and limits
Part II: Topology
Open and closed sets
Continuous functions
Composition of functions
Subsequences
Compactness
Existence of maximum
Uniform continuity
Connected sets and the intermediate value theorem
The Cantor set and fractals
Part III: Calculus
The derivative and the mean value theorem
The Riemann integral
The fundamental theorem of calculus
Sequences of functions
The Lebesgue theory
Infinite series sum_{n=1}^sigma a_n
Absolute convergence
Power series
Fourier series
Strings and springs
Convergence of Fourier series
The exponential function
Volumes of n-balls and the gamma function
Part IV: Metric spaces
Metric spaces
Analysis on metric spaces
Compactness in metric spaces
Ascoli's theorem
Partial solutions to exercises
Greek letters
Index
Details:
Publication Year: 2005
ISBN: 0-8218-3670-6
Paging: approximately 160 pp.
Binding: Hardcover