For many years Serge Lang has given talks to undergraduates on selected items in mathematics which could be extracted at a level understandable by students who have had calculus. Written in a conversational tone, Lang now presents a collection of those talks as a book. The talks could be given by faculty, but even better, they may be given by students in seminars run by the students themselves. Undergraduates, and even some high school students, will enjoy the talks which cover prime numbers, the abc conjecture, approximation theorems of analysis, Bruhat-Tits spaces, harmonic and symmetric...
For many years Serge Lang has given talks to undergraduates on selected items in mathematics which could be extracted at a level understandable by stu...
In 1988 Shafarevich asked me to write a volume for the Encyclopaedia of Mathematical Sciences on Diophantine Geometry. I said yes, and here is the volume. By definition, diophantine problems concern the solutions of equations in integers, or rational numbers, or various generalizations, such as finitely generated rings over Z or finitely generated fields over Q. The word Geometry is tacked on to suggest geometric methods. This means that the present volume is not elementary. For a survey of some basic problems with a much more elementary approach, see La 9Oc]. The field of diophantine...
In 1988 Shafarevich asked me to write a volume for the Encyclopaedia of Mathematical Sciences on Diophantine Geometry. I said yes, and here is the vol...
From the reviews "This book gives a thorough introduction to several theories that are fundamental to research on modular forms. Most of the material, despite its importance, had previously been unavailable in textbook form. Complete and readable proofs are given... In conclusion, this book is a welcome addition to the literature for the growing number of students and mathematicians in other fields who want to understand the recent developments in the theory of modular forms." #Mathematical Reviews# "This book will certainly be indispensable to all those wishing to get an...
From the reviews "This book gives a thorough introduction to several theories that are fundamental to research on modular forms. Most of the ma...
The worthy purpose of this text is to provide a complete, self-contained development of the trace formula and theta inversion formula for SL(2, Z i])SL(2, C). Unlike other treatments of the theory, the approach taken here is to begin with the heat kernel on SL(2, C) associated to the invariant Laplacian, which is derived using spherical inversion. The heat kernel on the quotient space SL(2, Z i])SL(2, C) is arrived at through periodization, and further expanded in an eigenfunction expansion. A theta inversion formula is obtained by studying the trace of the heat kernel. Following the...
The worthy purpose of this text is to provide a complete, self-contained development of the trace formula and theta inversion formula for SL(2, Z i...
These are notes of lectures on Nevanlinna theory, in the classical case of meromorphic functions, and the generalization by Carlson-Griffith to equidimensional holomorphic maps using as domain space finite coverings of Cresp. Cn. Conjecturally best possible error terms are obtained following a method of Ahlfors and Wong. This is especially significant when obtaining uniformity for the error term w.r.t. coverings, since the analytic yields case a strong version of Vojta's conjectures in the number-theoretic case involving the theory of heights. The counting function for...
These are notes of lectures on Nevanlinna theory, in the classical case of meromorphic functions, and the generalization by Carlson-Griffith to equidi...
Examines how analytic number theory and part of the spectral theory of operators are being merged into a more general theory of regularized products of certain sequences satisfying a few basic axioms. This monograph explains how the new theory can be applied to ergodic theory and dynamical systems.
Examines how analytic number theory and part of the spectral theory of operators are being merged into a more general theory of regularized products o...
The theory of explicit formulas for regularized products and series forms a natural continuation of the analytic theory developed in LNM 1564. These explicit formulas can be used to describe the quantitative behavior of various objects in analytic number theory and spectral theory. The present book deals with other applications arising from Gaussian test functions, leading to theta inversion formulas and corresponding new types of zeta functions which are Gaussian transforms of theta series rather than Mellin transforms, and satisfy additive functional equations. Their wide range of...
The theory of explicit formulas for regularized products and series forms a natural continuation of the analytic theory developed in LNM 1564. These e...
In 1988 Shafarevich asked me to write a volume for the Encyclopaedia of Mathematical Sciences on Diophantine Geometry. I said yes, and here is the volume. By definition, diophantine problems concern the solutions of equations in integers, or rational numbers, or various generalizations, such as finitely generated rings over Z or finitely generated fields over Q. The word Geometry is tacked on to suggest geometric methods. This means that the present volume is not elementary. For a survey of some basic problems with a much more elementary approach, see La 9Oc]. The field of diophantine...
In 1988 Shafarevich asked me to write a volume for the Encyclopaedia of Mathematical Sciences on Diophantine Geometry. I said yes, and here is the vol...
For the most part the authors are concerned with SLn(R) and with invariant differential operators, the invarinace being with respect to various subgroups. To a large extent, this book carries out the general results of Harish-Chandra.
For the most part the authors are concerned with SLn(R) and with invariant differential operators, the invarinace being with respect to various subgro...
This book contains essential material that every graduate student must know. Written with Serge Lang's inimitable wit and clarity, the volume introduces the reader to manifolds, differential forms, Darboux's theorem, Frobenius, and all the central features of the foundations of differential geometry. Lang lays the basis for further study in geometric analysis, and provides a solid resource in the techniques of differential topology. The book will have a key position on my shelf. -Steven Krantz, Washington University in St. Louis This is an elementary, finite dimensional version of the...
This book contains essential material that every graduate student must know. Written with Serge Lang's inimitable wit and clarity, the volume introduc...
