DATE: Tuesday, October 20 (2009), at 3:00pm
PLACE: LIT 305
SPEAKER: Krishnaswami Alladi
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TITLE:
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The Moebius function and integers without small
prime factors
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ABSTRACT:
We shall discuss my paper
"Asymptotic estimates of sums involving the Moebius function"
Journal of Number Theory, 14 (1982), 86-98
in which the sum of the Moebius function over integers n<x
all of whose prime factors are >y is analyzed. We shall obtain
asymptotic estimates that are uniform in y by studying a function
of α=lox/logy that satisfies a difference differential equation,
and discuss some novel applications in prime number theory.
Interestingly, this sum of the Moebius function is closely related
to the function ψ(x,y) - the number of integers <x all of whose
prime factors are <y.
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