The distribution of prime ends.
نویسندگان
چکیده
منابع مشابه
On Prime Ends and Local Connectivity
Let U ⊂ Ĉ be a simply connected domain whose complement K = Ĉ \ U contains more than one point. We show that the impression of a prime end of U contains at most two points at which K is locally connected. This is achieved by establishing a characterization of local connectivity of K at a point z0 ∈ ∂U in terms of the prime ends of U whose impressions contain z0 and then invoking a result of Urs...
متن کاملThe Distribution of Prime Numbers
The prime number theorem tells us that π(x), the number of primes below x, is ∼ x/ logx. Equivalently, if pn denotes the n-th smallest prime number then pn ∼ n logn. What is the distribution of the gaps between consecutive primes, pn+1 − pn? We have just seen that pn+1 − pn is approximately logn “on average”. How often do we get a gap of size 2 logn, say; or of size 1 2 logn? One way to make th...
متن کاملThe Distribution of Prime Numbers
Preface These notes cover the material for the graduate course with the same title that I taught at the University of Texas at Austin during the Spring 2005 semester. They draw heavily on The Distribution of Prime Numbers by M. Huxley and Multiplicative Number Theory by H. Davenport (as revised by H. L. Montgomery). I also acknowledge the use of notes by Jeff Vaaler and numerous discussions wit...
متن کاملNote on the Distribution of Prime Numbers
1. E. Cartan, " Les groupes reels simples finis et continus ", Ann. Ec Norm., 31 (1914), 263-355. 2; , " Sur certaines formes riemanniennes remarquables des geometries a groupe fondamental simple", Ann. Ec. Norm., t.44 (1927), 345-467. 3. , La thSorie des groupes finis el continus et I'analysis situs, Memorial Sc. Math. 62 (Gauthier-Villars, 1930). 4. C. Chevalley, Theory of Lie Groups (Princet...
متن کاملEvasiveness and the Distribution of Prime Numbers
A Boolean function on N variables is called evasive if its decision-tree complexity is N . A sequence Bn of Boolean functions is eventually evasive if Bn is evasive for all sufficiently large n. We confirm the eventual evasiveness of several classes of monotone graph properties under widely accepted number theoretic hypotheses. In particular we show that Chowla’s conjecture on Dirichlet primes ...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1960
ISSN: 0026-2285
DOI: 10.1307/mmj/1028998344