Arithmetic Functions and Integer Products

Elliott, Peter D. T. A.:

ISBN 10: 3540960945 / ISBN 13: 9783540960942

Published by New York; Berlin; Heidelberg; Tokyo: Springer-Verlag, 1985

About this Item

XV, 461 Seiten Mit 2 Abbildungen. - Innen sehr sauber. Hardcover, Pappeinband, mit den üblichen Bibliotheks-Markierungen, Stempeln und Einträgen, innen wie außen, siehe Bilder. Rücken verblasst. Innengelenk unten angebrochen. MIG-09-01A|A58 Sprache: Englisch Gewicht in Gramm: 850.

Seller Inventory # 87941

Bibliographic Details

• Title: Arithmetic Functions and Integer Products
• Publisher: New York; Berlin; Heidelberg; Tokyo: Springer-Verlag
• Publication Date: 1985
• Language: English
• ISBN 10: 3540960945
• ISBN 13: 9783540960942
• Binding: 24 x 16 cm
• Edition: 1. Auflage.
• Condition: Befriedigend
• Seller catalogs:
  • Modernes Antiquariat

About this title

Synopsis

Every 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.