** EVENT LISTSERV UPDATE **
 
                            --Pure Mathematics Seminar
 
                                       MATH
 
                       Thursday, 30 October 1997 at 3:30PM
 
                                   K9509 (SFU)
 
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                   Sums of Fractional Parts {n alpha + gamma}.
 
                                   Chris Pinner
 
                      Flinders and the University of Ottawa
 

                                     ABSTRACT
 
      I will talk about the behaviour of sums of the form
     C(m,alpha,gamma)=\sum_{n\leq m} ( \{n\alpha +\gamma \}-1/2 ) where
     alpha is a real irrational, gamma is a real in [0,1), and as usual
     {x}=x-[x]  denotes the fractional part of x. In particular for a fixed
     alpha I am interested in conditions on gamma which make these sums
     bounded from above or bounded from below for all m. As in the
     homogeneous case gamma=0 these sums are always unbounded in absolute
     value, so one-sided boundedness is the most one can ask for here. 

     Sums of this type occur in estimating the number of lattice points in
     a triangle.

 
 UBC/SFU NUMBER THEORY SEMINAR
 
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 Talk Sponsored by:    CECM

 For Additional Information, Contact:
    Name:    Peter Borwein
    E-mail:  pborwein@cs.sfu.ca
    Phone:   (604) 291-4376