Ber Einige Neuere Fortschritte Der Additiven Zahlentheorie
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Ber Einige Neuere Fortschritte Der Additiven Zahlentheorie
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Author : Edmund Landau
language : de
Publisher:
Release Date : 1937
Ber Einige Neuere Fortschritte Der Additiven Zahlentheorie written by Edmund Landau and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1937 with Forms (Mathematics). categories.
Additive Zahlen Theorie
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Author : Edmund Landau
language : de
Publisher:
Release Date : 1964
Additive Zahlen Theorie written by Edmund Landau and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Forms (Mathematics) categories.
Ber Einige Neuere Fortschritte Der Additiven Zahlentheorie
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Author : Edmund Landau
language : en
Publisher:
Release Date : 1964
Ber Einige Neuere Fortschritte Der Additiven Zahlentheorie written by Edmund Landau and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with categories.
Ber Einige Neuere Fortschritte Der Additiven Zahlentheorie
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Author : Edmund Landau (Mathématicien, Allemagne)
language : de
Publisher:
Release Date : 1937
Ber Einige Neuere Fortschritte Der Additiven Zahlentheorie written by Edmund Landau (Mathématicien, Allemagne) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1937 with categories.
Additive Zahlentheorie
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Author : Hans-H. Ostmann
language : de
Publisher: Springer-Verlag
Release Date : 2013-07-02
Additive Zahlentheorie written by Hans-H. Ostmann and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-02 with Mathematics categories.
Bereits seit längerer Zeit hat sich die additive Zahlentheorie als gesonderter Zweig innerhalb der Zahlentheorie herausgebildet; aber erst in den letzten Jahrzehnten hat dieses Gebiet neue Antriebe erhalten. In der klassischen additiven Zahlentheorie waren die Untersuchungs objekte im wesentlichen solche Fragestellungen, die an ganz spezielle Zahlenmengen geknüpft sind, wie etwa das GOLDBAcHsche oder das WARINGSche Problem. Diese bei den Probleme waren es aber auch, die den Anstoß zu einer neuen Entwicklung in der additiven Zahlentheorie gaben, als 1930 SCHNIRELMANN in seiner fundamentalen Arbeit "über additive Eigenschaften von Zahlen" [lJ einen neuen Zugang zu den ge nannten Problemen fand. SCHNIRELMANN entwickelte nämlich zunächst eine Theorie, die ganz von der speziellen Natur der Primzahlen bzw. der k-ten Potenzen absah und sich allgemein auf Mengen natürlicher Zahlen bezog. Jeder solchen Menge wird eine reelle Zahl, die "Dichte" zuge ordnet, die in gewissem Sinn ein Maß dafür ist, welcher Anteil aus der Gesamtheit aller natürlichen Zahlen der gegebenen Menge angehört. An Stelle der arithmetischen Natur der Zahlenmenge tritt also ein in dieser Weise zu verstehender metrischer Gesichtspunkt. Indem ferner noch die Summe solcher Mengen eingeführt wurde, zeigte sich, daß bereits in großer Allgemeinheit wesentliche Aussagen gemacht werden konnten. In Anschluß an SCHNIRELMANN hat diese allgemeine Theorie der Zahl mengen immer neue Impulse erhalten; somit schien für den vorliegen den Bericht ziemlich zwangsläufig eine grobe Gliederung durch die Stichworte "Summe", "Dichte", bzw. "spezielle Mengen" gegeben zu sein.
Additive Number Theory The Classical Bases
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Author : Melvyn B. Nathanson
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Additive Number Theory The Classical Bases written by Melvyn B. Nathanson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
[Hilbert's] style has not the terseness of many of our modem authors in mathematics, which is based on the assumption that printer's labor and paper are costly but the reader's effort and time are not. H. Weyl [143] The purpose of this book is to describe the classical problems in additive number theory and to introduce the circle method and the sieve method, which are the basic analytical and combinatorial tools used to attack these problems. This book is intended for students who want to lel?Ill additive number theory, not for experts who already know it. For this reason, proofs include many "unnecessary" and "obvious" steps; this is by design. The archetypical theorem in additive number theory is due to Lagrange: Every nonnegative integer is the sum of four squares. In general, the set A of nonnegative integers is called an additive basis of order h if every nonnegative integer can be written as the sum of h not necessarily distinct elements of A. Lagrange 's theorem is the statement that the squares are a basis of order four. The set A is called a basis offinite order if A is a basis of order h for some positive integer h. Additive number theory is in large part the study of bases of finite order. The classical bases are the squares, cubes, and higher powers; the polygonal numbers; and the prime numbers. The classical questions associated with these bases are Waring's problem and the Goldbach conjecture.
Ueber Einige Neuere Fortschritte Der Additiven Zahlentheorie
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Author : Edmund Landau
language : de
Publisher:
Release Date : 1937
Ueber Einige Neuere Fortschritte Der Additiven Zahlentheorie written by Edmund Landau and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1937 with Forms (Mathematics) categories.
Sequences
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Author : H. Halberstam
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Sequences written by H. Halberstam and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
THIS volume is concerned with a substantial branch of number theory of which no connected account appears to exist; we describe the general nature of the constituent topics in the introduction. Although some excellent surveys dealing with limited aspects of the subject under con sideration have been published, the literature as a whole is far from easy to study. This is due in part to the extent of the literature; it is necessary to thread one's way through a maze of results, a complicated structure of inter-relationships, and many conflicting notations. In addition, however, not all the original papers are free from obscurities, and consequently some of these papers are difficult (a few even exceed ingly difficult) to master. We try to give a readable and coherent account of the subject, con taining a cross-section of the more interesting results. We felt that it would have been neither practicable nor desirable to attempt a compre hensive account; we treat each aspect of the subject from some special point of view, and select results accordingly. Needless to say, this approach entails the omission of many interesting and important results (quite apart from defects in the selection due to errors of judgement on our part). Those results selected for inclusion are, however, proved in complete detail and without the assumption of any prior knowledge on the part of the reader.
Arithmetical Functions
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Author : Komaravolu Chandrasekharan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Arithmetical Functions written by Komaravolu Chandrasekharan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The 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. .
Diophantine Equations And Inequalities In Algebraic Number Fields
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Author : Yuan Wang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Diophantine Equations And Inequalities In Algebraic Number Fields written by Yuan Wang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The circle method has its genesis in a paper of Hardy and Ramanujan (see [Hardy 1])in 1918concernedwiththepartitionfunction andtheproblemofrep resenting numbers as sums ofsquares. Later, in a series of papers beginning in 1920entitled "some problems of'partitio numerorum''', Hardy and Littlewood (see [Hardy 1]) created and developed systematically a new analytic method, the circle method in additive number theory. The most famous problems in ad ditive number theory, namely Waring's problem and Goldbach's problem, are treated in their papers. The circle method is also called the Hardy-Littlewood method. Waring's problem may be described as follows: For every integer k 2 2, there is a number s= s(k) such that every positive integer N is representable as (1) where Xi arenon-negative integers. This assertion wasfirst proved by Hilbert [1] in 1909. Using their powerful circle method, Hardy and Littlewood obtained a deeper result on Waring's problem. They established an asymptotic formula for rs(N), the number of representations of N in the form (1), namely k 1 provided that 8 2 (k - 2)2 - +5. Here