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SUMMARY:Multiplicative Functions - Professor K. Soundararajan (Stanford Un
 iversity)
DTSTART:20070313T170000Z
DTEND:20070313T180000Z
UID:TALK6457@talks.cam.ac.uk
CONTACT:4993
DESCRIPTION:A multiplicative function $f: {\\Bbb N} \\to {\\Bbb C}$ is a \
 nfunction satisfying $f(mn)=f(m)f(n)$.  Many naturally occuring \nfunction
 s in number theory are multiplicative.  Over the last several \nyears\, An
 drew Granville and I have been studying various features of \nmultiplicati
 ve functions.  I will discuss some aspects of this work.  \nFor example\, 
 I will answer the question of how many numbers up to a \ngiven number $x$ 
 are quadratic residues (you are free to choose the \nprime $p$ so as to mi
 nimize the answer).  As another example\, I will \ndiscuss character sums 
 and a recent improvement of a classical \ninequality of Polya and Vinograd
 ov.
LOCATION:Wolfson Room (MR 2) Centre for Mathematical Sciences\, Wilberforc
 e Road\, Cambridge
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