An Arithmetical Theory of Certain Numerical Functions
Author: Eric Temple Bell
Publisher:
Published: 1915
Total Pages: 60
ISBN-13:
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Classical Theory of Arithmetic Functions
Author: R Sivaramakrishnan
Publisher: Routledge
Published: 2018-10-03
Total Pages: 416
ISBN-13: 135146051X
DOWNLOAD EBOOKThis volume focuses on the classical theory of number-theoretic functions emphasizing algebraic and multiplicative techniques. It contains many structure theorems basic to the study of arithmetic functions, including several previously unpublished proofs. The author is head of the Dept. of Mathemati
Introduction to the Arithmetic Theory of Automorphic Functions
Author: Gorō Shimura
Publisher: Princeton University Press
Published: 1971-08-21
Total Pages: 292
ISBN-13: 9780691080925
DOWNLOAD EBOOKThe theory of automorphic forms is playing increasingly important roles in several branches of mathematics, even in physics, and is almost ubiquitous in number theory. This book introduces the reader to the subject and in particular to elliptic modular forms with emphasis on their number-theoretical aspects. After two chapters geared toward elementary levels, there follows a detailed treatment of the theory of Hecke operators, which associate zeta functions to modular forms. At a more advanced level, complex multiplication of elliptic curves and abelian varieties is discussed. The main question is the construction of abelian extensions of certain algebraic number fields, which is traditionally called "Hilbert's twelfth problem." Another advanced topic is the determination of the zeta function of an algebraic curve uniformized by modular functions, which supplies an indispensable background for the recent proof of Fermat's last theorem by Wiles.
Higher Arithmetic
Author: Harold M. Edwards
Publisher: American Mathematical Soc.
Published: 2008
Total Pages: 228
ISBN-13: 9780821844397
DOWNLOAD EBOOKAmong the topics featured in this textbook are: congruences; the fundamental theorem of arithmetic; exponentiation and orders; primality testing; the RSA cipher system; polynomials; modules of hypernumbers; signatures of equivalence classes; and the theory of binary quadratic forms. The book contains exercises with answers.
Introduction to Arithmetical Functions
Author: Paul J. McCarthy
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 373
ISBN-13: 1461386209
DOWNLOAD EBOOKThe theory of arithmetical functions has always been one of the more active parts of the theory of numbers. The large number of papers in the bibliography, most of which were written in the last forty years, attests to its popularity. Most textbooks on the theory of numbers contain some information on arithmetical functions, usually results which are classical. My purpose is to carry the reader beyond the point at which the textbooks abandon the subject. In each chapter there are some results which can be described as contemporary, and in some chapters this is true of almost all the material. This is an introduction to the subject, not a treatise. It should not be expected that it covers every topic in the theory of arithmetical functions. The bibliography is a list of papers related to the topics that are covered, and it is at least a good approximation to a complete list within the limits I have set for myself. In the case of some of the topics omitted from or slighted in the book, I cite expository papers on those topics.
Number Theory in Function Fields
Author: Michael Rosen
Publisher: Springer Science & Business Media
Published: 2013-04-18
Total Pages: 355
ISBN-13: 1475760469
DOWNLOAD EBOOKEarly in the development of number theory, it was noticed that the ring of integers has many properties in common with the ring of polynomials over a finite field. The first part of this book illustrates this relationship by presenting analogues of various theorems. The later chapters probe the analogy between global function fields and algebraic number fields. Topics include the ABC-conjecture, Brumer-Stark conjecture, and Drinfeld modules.
Arithmetical Functions
Author: Komaravolu Chandrasekharan
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 244
ISBN-13: 3642500269
DOWNLOAD EBOOKThe plan of this book had its inception in a course of lectures on arithmetical functions given by me in the summer of 1964 at the Forschungsinstitut fUr Mathematik of the Swiss Federal Institute of Technology, Zurich, at the invitation of Professor Beno Eckmann. My Introduction to Analytic Number Theory has appeared in the meanwhile, and this book may be looked upon as a sequel. It presupposes only a modicum of acquaintance with analysis and number theory. The arithmetical functions considered here are those associated with the distribution of prime numbers, as well as the partition function and the divisor function. Some of the problems posed by their asymptotic behaviour form the theme. They afford a glimpse of the variety of analytical methods used in the theory, and of the variety of problems that await solution. I owe a debt of gratitude to Professor Carl Ludwig Siegel, who has read the book in manuscript and given me the benefit of his criticism. I have improved the text in several places in response to his comments. I must thank Professor Raghavan Narasimhan for many stimulating discussions, and Mr. Henri Joris for the valuable assistance he has given me in checking the manuscript and correcting the proofs. K. Chandrasekharan July 1970 Contents Chapter I The prime number theorem and Selberg's method § 1. Selberg's fonnula . . . . . . 1 § 2. A variant of Selberg's formula 6 12 § 3. Wirsing's inequality . . . . . 17 § 4. The prime number theorem. .
Certain Number-Theoretic Episodes In Algebra, Second Edition
Author: R Sivaramakrishnan
Publisher: CRC Press
Published: 2019-03-19
Total Pages: 273
ISBN-13: 1351023322
DOWNLOAD EBOOKThe book attempts to point out the interconnections between number theory and algebra with a view to making a student understand certain basic concepts in the two areas forming the subject-matter of the book.
Introduction to Analytic Number Theory
Author: Tom M. Apostol
Publisher: Springer Science & Business Media
Published: 2013-06-29
Total Pages: 352
ISBN-13: 1475755791
DOWNLOAD EBOOK"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages."-—MATHEMATICAL REVIEWS
Arithmetic Functions and Integer Products
Author: P.D.T.A. Elliott
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 469
ISBN-13: 1461385482
DOWNLOAD EBOOKEvery positive integer m has a product representation of the form where v, k and the ni are positive integers, and each Ei = ± I. A value can be given for v which is uniform in the m. A representation can be computed so that no ni exceeds a certain fixed power of 2m, and the number k of terms needed does not exceed a fixed power of log 2m. Consider next the collection of finite probability spaces whose associated measures assume only rational values. Let hex) be a real-valued function which measures the information in an event, depending only upon the probability x with which that event occurs. Assuming hex) to be non negative, and to satisfy certain standard properties, it must have the form -A(x log x + (I - x) 10g(I -x». Except for a renormalization this is the well-known function of Shannon. What do these results have in common? They both apply the theory of arithmetic functions. The two widest classes of arithmetic functions are the real-valued additive and the complex-valued multiplicative functions. Beginning in the thirties of this century, the work of Erdos, Kac, Kubilius, Turan and others gave a discipline to the study of the general value distribution of arithmetic func tions by the introduction of ideas, methods and results from the theory of Probability. I gave an account of the resulting extensive and still developing branch of Number Theory in volumes 239/240 of this series, under the title Probabilistic Number Theory.
