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Item Details
| Title:
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ARITHMETIC FUNCTIONS AND INTEGER PRODUCTS
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| By: |
P. D. T. A. Elliott |
| Format: |
Paperback |
| List price:
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£54.99 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
1461385504 |
| ISBN 13: |
9781461385509 |
| Publisher: |
SPRINGER-VERLAG NEW YORK INC. |
| Pub. date: |
18 October, 2011 |
| Edition: |
Softcover reprint of the original 1st ed. 1985 |
| Series: |
Grundlehren der mathematischen Wissenschaften 272 |
| Pages: |
461 |
| Description: |
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. |
| 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. |
| Illustrations: |
461 p. |
| Publication: |
US |
| Imprint: |
Springer-Verlag New York Inc. |
| Returns: |
Returnable |
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