{"product_id":"9780387960944","title":"Grundlehren der mathematischen Wissenschaften","description":"\u003ch1\u003eGrundlehren der mathematischen Wissenschaften\u003c\/h1\u003e \u003ch2\u003eElliott, P.D.T.A.\u003c\/h2\u003e \u003cp\u003eEvery 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.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 1984-11-20\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9780387960944\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-1-4613-8548-6\u003c\/p\u003e \u003cp\u003eDimensions: cm xcm\u003c\/p\u003e \u003cp\u003ePages: 461\u003c\/p\u003e ","brand":"Springer New York","offers":[{"title":"Default Title","offer_id":45379166142604,"sku":"9780387960944","price":89.1,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9780387960944.jpg?v=1771516023","url":"https:\/\/lateknightbooks.com\/products\/9780387960944","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}