DATE: Tuesday, November 10 (2009), at 3:00pm
PLACE: LIT 305
SPEAKER: Krishnaswami Alladi
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TITLE:
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Sums of the Moebius function and the Prime Number Theorem for Arithmetic Progressions
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ABSTRACT:
We will discuss my 1997 paper
Duality between prime factors and an application to
the prime number theorem for arithmetic progressions
J. Num Th. 9 (1977), 436-451.
in which a new duality identity between the smallest
and largest prime factors is established using the
Moebius function. Applications of this duality will
be discussed, most notably sums of the Moebius function
that are intimately connected with the prime number
theorem for arithmetic progressions. The classical
results involve sums of the Moebius function multiplied
by Dirichlet characters; here the novelty lies in
studying the Moebius function with the largest and
smallest prime factors lying in arithmetic progressions.
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