DATE: Tuesday, November 3 (2009), at 3:00pm
PLACE: LIT 305
SPEAKER: Krishnaswami Alladi
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TITLE:
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Sums of the Moebius function over integers with small prime factors
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ABSTRACT:
We will discuss my paper
Asymptotic estimates of sums involving the Moebius
function -II, Transactions AMS 222 (1982), 87-105
in which uniform estimates for the sum of the Moebius
function over integers <x having all prime factors <y
are obtained. This is the conjugate problem compared
to the sums of the Moebius function over integers free
of small prime factors. Here too the analysis of a function
satisfying a difference-differential equation is required,
but the outcome is very different: This sum of the Moebius
function changes sign infinitely often and the study of
sign changes leads to connections with fundamental results
in prime number theory. Analytic methods are employed
to partially settle a problem of Erdos on the Moebius function.
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