| 期刊全稱(chēng) | Arithmetic Functions and Integer Products | | 影響因子2023 | P. D. T. A. Elliott | | 視頻video | http://file.papertrans.cn/162/161592/161592.mp4 | | 學(xué)科分類(lèi) | Grundlehren der mathematischen Wissenschaften | | 圖書(shū)封面 |  | | 影響因子 | 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 | | Pindex | Book 1985 |
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