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Topics in the Theory of Quadratic Residues
by Steve Wright - arXiv , 2014
Beginning with Gauss, the study of quadratic residues and nonresidues has subsequently led directly to many of the ideas and techniques that are used everywhere in number theory today, and the primary goal of these lectures is to use this study ...
Geometry of Numbers with Applications to Number Theory
by Pete L. Clark - University of Georgia , 2013
The goal is to find and explore open questions in both geometry of numbers -- e.g. Lattice Point Enumerators, the Ehrhart-Polynomial, Minkowski's Convex Body Theorems, Minkowski-Hlawka Theorem, ... -- and its applications to number theory.
Lectures On Irregularities Of Distribution
by Wolfgang M. Schmidt - Tata Institute of Fundamental Research , 1977
The theory of Irregularities of Distribution began as a branch of Uniform Distributions, but is of independent interest. In these lectures the author restricted himself to distribution problems with a geometric interpretation.
Lectures on Shimura Varieties
by A. Genestier, B.C. Ngo , 2006
The goal of these lectures is to explain the representability of moduli space abelian varieties with polarization, endomorphism and level structure, due to Mumford and the description of the set of its points over a finite field, due to Kottwitz.
Introduction to Shimura Varieties
by J.S. Milne , 2004
This is an introduction to the theory of Shimura varieties, or, in other words, to the arithmetic theory of automorphic functions and holomorphic automorphic forms. Because of their brevity, many proofs have been omitted or only sketched.
Elliptic Curves over Function Fields
by Douglas Ulmer - arXiv , 2011
The focus is on elliptic curves over function fields over finite fields. We explain the main classical results on the Birch and Swinnerton-Dyer conjecture in this context and its connection to the Tate conjecture about divisors on surfaces.
Harmonic Analysis, the Trace Formula, and Shimura Varieties
by J. Arthur, D. Ellwood, R. Kottwitz - American Mathematical Society , 2005
The goal of this volume is to provide an entry point into the challenging field of the modern theory of automorphic forms. It is directed on the one hand at graduate students and professional mathematicians who would like to work in the area.
Notes on Fermionic Fock Space for Number Theorists
by Greg W. Anderson - The University of Arizona , 2000
This is a compilation of exercises, worked examples and key references that the author compiled in order to help readers learn their way around fermionic Fock space. The text is suitable for use by graduate students with an interest in number theory.
Modular Forms, Hecke Operators, and Modular Abelian Varieties
by Kenneth A. Ribet, William A. Stein - University of Washington , 2003
Contents: The Main objects; Modular representations and algebraic curves; Modular Forms of Level 1; Analytic theory of modular curves; Modular Symbols; Modular Forms of Higher Level; Newforms and Euler Products; Hecke operators as correspondences...
Langlands Correspondence for Loop Groups
by Edward Frenkel - Cambridge University Press , 2007
This book provides a review of an important aspect of the geometric Langlands program - the role of representation theory of affine Kac-Moody algebras. It provides introductions to such notions as vertex algebras, the Langlands dual group, etc.
Essays on the Theory of Numbers
by Richard Dedekind - The Open Court Publishing , 1901
This is a book combining two essays: 'Continuity and irrational numbers' - Dedekind's way of defining the real numbers from rational numbers; and 'The nature and meaning of numbers' where Dedekind offers a precise explication of the natural numbers.
Algorithms for Modular Elliptic Curves
by J. E. Cremona - Cambridge University Press , 1992
The author describes the construction of modular elliptic curves giving an algorithm for their computation. Then algorithms for the arithmetic of elliptic curves are presented. Finally, the results of the implementations of the algorithms are given.
Arithmetic Duality Theorems
by J.S. Milne - BookSurge Publishing , 2006
This book, intended for research mathematicians, proves the duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry, for example, in the proof of Fermat's Last Theorem.
by Edward Nelson - Princeton Univ Pr , 1987
The book based on lecture notes of a course given at Princeton University in 1980. From the contents: the impredicativity of induction, the axioms of arithmetic, order, induction by relativization, the bounded least number principle, and more.
Geometric Theorems and Arithmetic Functions
by Jozsef Sandor - American Research Press , 2002
Contents: on Smarandache's Podaire theorem, Diophantine equation, the least common multiple of the first positive integers, limits related to prime numbers, a generalized bisector theorem, values of arithmetical functions and factorials, and more.
The Smarandache Function
by C. Dumitrescu, V. Seleacu - Erhus University Press , 1996
The function in the title is originated from the Romanian mathematician Florentin Smarandache, who has significant contributions in mathematics and literature. This text introduces the Smarandache function and discusses its generalisations.
Comments and topics on Smarandache notions and problems
by Kenichiro Kashihara - Erhus University Press , 1996
An examination of some of the problems posed by Florentin Smarandache. The problems are from different areas, such as sequences, primes and other aspects of number theory. The problems are solved in the book, or the author raises new questions.
On Some of Smarandache's Problems
by Krassimir Atanassov - Erhus Univ Pr , 1999
A collection of 27 Smarandache's problems which the autor solved by 1999. 22 problems are related to different sequences, 4 problems are proved, modifications of two problems are formulated, and counterexamples to two of the problems are constructed.
Collections of Problems on Smarandache Notions
by Charles Ashbacher - Erhus University Press , 1996
This text deals with some advanced consequences of the Smarandache function. The reading of this book is a form of mindjoining, where the author tries to create the opportunity for a shared experience of an adventure.
A set of new Smarandache functions, sequences and conjectures in number theory
by Felice Russo - American Research Press , 2000
The fascinating Smarandache's universe is halfway between the recreational mathematics and the number theory. This book presents new Smarandache functions, conjectures, solved and unsolved problems, new type sequences and new notions in number theory.
Pluckings from the tree of Smarandache: Sequences and functions
by Charles Ashbacher - American Research Press , 1998
The third book in a series exploring the set of problems called Smarandache Notions. This work delves more deeply into the mathematics of the problems, the level of difficulty here will be somewhat higher than that of the previous books.
An Introduction to the Smarandache Function
by Charles Ashbacher - Erhus Univ Pr , 1995
In the 1970's a Rumanian mathematician Florentin Smarandache created a new function in number theory, which consequences encompass many areas of mathematics.The purpose of this text is to examine some of those consequences.