How Long to Read Probabilistic Number Theory II

How Long Does it Take to Read Probabilistic Number Theory II?

It takes the average reader 6 hours and 22 minutes to read Probabilistic Number Theory II by P.D.T.A. Elliott

Assuming a reading speed of 250 words per minute. Learn more

Description

In this volume we study the value distribution of arithmetic functions, allowing unbounded renormalisations. The methods involve a synthesis of Probability and Number Theory; sums of independent infinitesimal random variables playing an important role. A central problem is to decide when an additive arithmetic function fin) admits a renormalisation by real functions a(x) and {3(x) > 0 so that asx ~ 00 the frequencies vx(n;f (n) - a(x) :s;; z {3 (x) ) converge weakly; (see Notation). In contrast to volume one we allow {3(x) to become unbounded with x. In particular, we investigate to what extent one can simulate the behaviour of additive arithmetic functions by that of sums of suit ably defined independent random variables. This fruiful point of view was intro duced in a 1939 paper of Erdos and Kac. We obtain their (now classical) result in Chapter 12. Subsequent methods involve both Fourier analysis on the line, and the appli cation of Dirichlet series. Many additional topics are considered. We mention only: a problem of Hardy and Ramanujan; local properties of additive arithmetic functions; the rate of convergence of certain arithmetic frequencies to the normal law; the arithmetic simulation of all stable laws. As in Volume I the historical background of various results is discussed, forming an integral part of the text. In Chapters 12 and 19 these considerations are quite extensive, and an author often speaks for himself.

How long is Probabilistic Number Theory II?

Probabilistic Number Theory II by P.D.T.A. Elliott is 375 pages long, and a total of 95,625 words.

This makes it 127% the length of the average book. It also has 117% more words than the average book.

How Long Does it Take to Read Probabilistic Number Theory II Aloud?

The average oral reading speed is 183 words per minute. This means it takes 8 hours and 42 minutes to read Probabilistic Number Theory II aloud.

What Reading Level is Probabilistic Number Theory II?

Probabilistic Number Theory II is suitable for students ages 12 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Probabilistic Number Theory II?

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