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SUMMARY:Multiplicative functions (Kuwait Lecture) - K. Soundararajan (Stan
 ford)
DTSTART:20070313T170000Z
DTEND:20070313T180000Z
UID:TALK5776@talks.cam.ac.uk
CONTACT:Ben Green
DESCRIPTION: A multiplicative function f: N -> C is a \nfunction satisfyin
 g f(mn)=f(m)f(n).  Many naturally occuring \nfunctions in number theory ar
 e multiplicative.  Over the last several \nyears\, Andrew Granville and I 
 have been studying various features of \nmultiplicative functions.  I will
  discuss some aspects of this work.  \nFor example\, I will answer the que
 stion of how many numbers up to a \ngiven number x are quadratic residues 
 (you are free to choose the \nprime p so as to minimize the answer).  As a
 nother example\, I will \ndiscuss character sums and a recent improvement 
 of a classical \ninequality of P&oacute\;lya and Vinogradov.\n
LOCATION:MR2\, CMS
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