Series: Springer Proceedings in Mathematics & Statistics, Vol. 188
Celebrating one of the leading figures in contemporary number theory John H. Coates
on the occasion of his 70th birthday, this collection of contributions covers a range of
topics in number theory, concentrating on the arithmetic of elliptic curves, modular forms,
and Galois representations. Several of the contributions in this volume were presented at
the conference Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the
70th birthday of John Coates in Cambridge, March 25-27, 2015. The main unifying theme
is Iwasawa theory, a field that John Coates himself has done much to create.
This collection is indispensable reading for researchers in Iwasawa theory, and is
interesting and valuable for those in many related fields.
1st ed. 2016, IX, 466 p. 14 illus., 1 illus. in color.
Hardcover
ISBN 978-3-319-45031-5
Series: Lecture Notes in Mathematics, Vol. 2170
* Introduces a cutting-edge method for effective construction of
symmetry breaking operators for branching rules in representation theory
* Includes hot topics of conformal geometry and global analysis as
applications of representation theory
* Provides the complete classification of all conformally equivariant
differential operators on forms on the model space (Sn, Sn-1)
This work is the first systematic study of all possible conformally covariant differential
operators transforming differential forms on a Riemannian manifold X into those on a
submanifold Y with focus on the model space (X, Y) = (Sn, Sn-1).
The authors give a complete classification of all such conformally covariant differential
operators, and find their explicit formula in the flat coordinates in terms of basic
operators in differential geometry and classical hypergeometric polynomials. Resulting
families of operators are natural generalizations of the Rankin?Cohen brackets for
modular forms and Juhl's operators from conformal holography. The matrix-valued
factorization identities among all possible combinations of conformally covariant
differential operators are also established.
The main machinery of the proof relies on the "F-method" recently introduced and
developed by the authors. It is a general method to construct intertwining operators
between C∞-induced representations or to find singular vectors of Verma modules in the
context of branching rules, as solutions to differential equations on the Fourier transform
side. The book gives a new extension of the F-method to the matrix-valued case in the
general setting, which could be applied to other problems as well.
This book offers a self-contained introduction to the analysis of symmetry
breaking operators for infinite-dimensional representations of reductive Lie groups. This
feature will be helpful for active scientists and accessible to graduate students and young
researchers in differential geometry, representation theory, and theoretical physics.
1st ed. 2016, IX, 192 p.
Softcover
ISBN 978-981-10-2656-0
Series: Lecture Notes in Mathematics, Vol. 2171
* Illustrates how the study of quadratic residues led directly to the
development of fundamental methods in elementary, algebraic, and
analytic number theory
* Presents in detail seven proofs of the Law of Quadratic Reciprocity,
with an emphasis on the six proofs which Gauss published
* Discusses in some depth the historical development of the study of
quadratic residues and non-residues
This book offers an account of the classical theory of quadratic residues and non-residues
with the goal of using that theory as a lens through which to view the development of
some of the fundamental methods employed in modern elementary, algebraic, and
analytic number theory.
The first three chapters present some basic facts and the history of quadratic residues and
non-residues and discuss various proofs of the Law of Quadratic Reciprosity in depth,
with an emphasis on the six proofs that Gauss published. The remaining seven chapters
explore some interesting applications of the Law of Quadratic Reciprocity, prove some
results concerning the distribution and arithmetic structure of quadratic residues and
non-residues, provide a detailed proof of Dirichlet’s Class-Number Formula, and discuss
the question of whether quadratic residues are randomly distributed. The text is a
valuable resource for graduate and advanced undergraduate students as well as for
mathematicians interested in number theory.
1st ed. 2016, XX, 210 p. 20 illus.
Softcover
ISBN 978-3-319-45954-7
Series: Springer Series in Statistics
* Brings together assorted methods concerning measurement error
or misclassification in a single text, including updates of recent
developments for a variety of settings
* Presents both statistical theory and applications in a coherent and
systematic manner
* Highlights the essence of commonly used modeling and inference
strategies
* Includes self-contained material of an individual topic in each
chapter
* Provides exercises, discussion questions, and bibliographic notes at
the end of each chapter to supplement the development in the text
This monograph on measurement error and misclassification covers a broad range of
problems and emphasizes unique features in modeling and analyzing problems arising
from medical research and epidemiological studies. Many measurement error and
misclassification problems have been addressed in various fields over the years as well
as with a wide spectrum of data, including event history data (such as survival data and
recurrent event data), correlated data (such as longitudinal data and clustered data),
multi-state event data, and data arising from case-control studies. Statistical Analysis with
Measurement Error or Misclassification: Strategy, Method and Application brings together
assorted methods in a single text and provides an update of recent developments for a
variety of settings. Measurement error effects and strategies of handling mismeasurement
for different models are closely examined in combination with applications to specific
problems.
Readers with diverse backgrounds and objectives can utilize this text. Familiarity with
inference methods?such as likelihood and estimating function theory?or modeling
schemes in varying settings?such as survival analysis and longitudinal data analysis?
can result in a full appreciation of the material, but it is not essential since each chapter
provides basic inference frameworks and background information on an individual topic
to ease the access of the material. The text is presented in a coherent and self-contained
manner and highlights the essence of commonly used modeling and inference methods.
1st ed. 2016, VIII, 498 p. 16 illus., 1 illus. in color.
Hardcover
ISBN 978-1-4939-6638-7
Series: Fields Institute Communications, Vol. 78
* Discusses a diverse range of state-of-the-art topics in time series
analysis
* Contains contributions from a number of researchers renowned
for their time series work
* Covers applications, methodologies, and theory
* Accessible to researchers, practitioners, and graduate students
This volume reviews and summarizes some of A. I. McLeod's significant contributions
to time series analysis. It also contains original contributions to the field and to related
areas by participants of the festschrift held in June 2014 and friends of Dr. McLeod.
Covering a diverse range of state-of-the-art topics, this volume well balances applied
and theoretical research across fourteen contributions by experts in the field. It will be
of interest to researchers and practitioners in time series, econometricians, and graduate
students in time series or econometrics, as well as environmental statisticians, data
scientists, statisticians interested in graphical models, and researchers in quantitative risk
management.
1st ed. 2016, VII, 271 p. 37 illus., 7 illus. in color.
Hardcover
ISBN 978-1-4939-6567-0
Series: Progress in Mathematics, Vol. 319
* A tribute to Friedrich Hirzebruch, the founder of the Arbeitstagung
conference series, by renowned mathematicians
* Only the second proceedings volume to be published for the
Arbeitstagung
* Papers cover a wide range of current topics in pure mathematics
This volume contains selected papers authored by speakers and participants of the 2013
Arbeitstagung, held at the Max Planck Institute for Mathematics in Bonn, Germany, from
May 22-28. The 2013 meeting (and this resulting proceedings) was dedicated to the
memory of Friedrich Hirzebruch, who passed away on May 27, 2012.
Hirzebruch organized the first Arbeitstagung in 1957 with a unique concept that would become its most
distinctive feature: the program was not determined beforehand by the organizers, but
during the meeting by all participants in an open discussion. This ensured that the talks
would be on the latest developments in mathematics and that many important results
were presented at the conference for the first time. Written by leading mathematicians,
the papers in this volume cover various topics from algebraic geometry, topology,
analysis, operator theory, and representation theory and display the breadth and depth of
pure mathematics that has always been characteristic of the Arbeitstagung.
1st ed. 2016, IV, 360 p. 23 illus., 12 illus. in color.
Hardcover
ISBN 978-3-319-43646-3