Conductor (class field theory): Difference between revisions

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en>Spectral sequence
The prime p was introduced but never referred back to. Looking at Milne's textbook that was referenced, you see that p only played an auxiliary role in the calculation.
 
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In [[number theory]], the '''Erdős arcsine law''', named after [[Paul Erdős]], states that the [[prime number|prime]] [[divisor]]s of a number have a distribution related to the [[arcsine distribution]].
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Specifically, say that the ''j''th prime factor ''p'' of a given number ''n'' (in the sorted sequence of distinct prime factors) is "small" when {{nowrap|log log ''p'' < ''j''}}.
Then, for any fixed parameter ''u'', in the limit as ''x'' goes to infinity, the proportion of the integers ''n'' less than ''x'' that have fewer than {{nowrap|''u'' log log ''n''}} small prime factors converges to
:<math>\frac{2}{\pi}\arcsin{\sqrt{u}}.</math>
 
==References==
*{{Citation | last1=Manstavičius | first1=E. | title=Probability theory and mathematical statistics (Vilnius, 1993) | publisher=TEV | location=Vilnius | mr=1649597 | year=1994 | chapter=A proof of the Erdős arcsine law | pages=533–539}}
 
{{DEFAULTSORT:Erdos Arcsine Law}}
[[Category:Number theory]]
 
{{numtheory-stub}}

Latest revision as of 09:16, 27 April 2014

My name's Lula Thigpen but everybody calls me Lula. I'm from Austria. I'm studying at the high school (final year) and I play the Mandolin for 5 years. Usually I choose music from my famous films ;).
I have two sister. I love Origami, watching TV (The Simpsons) and Darts.

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