Arithmetic Functions and Integer Products is popular PDF and ePub book, written by P.D.T.A. Elliott in 2012-12-06, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Arithmetic Functions and Integer Products can be Read Online from any device for your convenience.
Arithmetic Functions and Integer Products Book PDF Summary
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.
Detail Book of Arithmetic Functions and Integer Products PDF
- Author : P.D.T.A. Elliott
- Release : 06 December 2012
- Publisher : Springer Science & Business Media
- ISBN : 9781461385486
- Genre : Mathematics
- Total Page : 469 pages
- Language : English
- PDF File Size : 15,9 Mb
If you're still pondering over how to secure a PDF or EPUB version of the book Arithmetic Functions and Integer Products by P.D.T.A. Elliott, don't worry! All you have to do is click the 'Get Book' buttons below to kick off your Download or Read Online journey. Just a friendly reminder: we don't upload or host the files ourselves.