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 ...
Read More
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.
Read Less
Add this copy of Arithmetic Functions and Integer Products (Grundlehren to cart. $29.00, good condition, Sold by HPB-Red rated 5.0 out of 5 stars, ships from Dallas, TX, UNITED STATES, published 1984 by Springer.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Good. Connecting readers with great books since 1972! Used textbooks may not include companion materials such as access codes, etc. May have some wear or writing/highlighting. We ship orders daily and Customer Service is our top priority!
Add this copy of Arithmetic Functions and Integer Products (Grundlehren to cart. $50.00, good condition, Sold by Powell's Books Chicago rated 5.0 out of 5 stars, ships from Chicago, IL, UNITED STATES, published 1984 by Springer.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Good. 1984. Hardcover. Cloth, no dj. Binding beginning to separate at front hinge, some gauze visible. Despite this flaw, text block is firm and clean, and volume is in otherwise very good condition. Good. (Subject: Mathematics).
Add this copy of Arithmetic Functions and Integer Products (Grundlehren to cart. $62.19, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 1984 by Springer.
Add this copy of Arithmetic Functions and Integer Products (Grundlehren to cart. $88.67, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2011 by Springer.
