Richard McIntoshAffiliation: University of Regina, Canada Email: mcintosh@math.uregina.ca Title Of Talk: Divisor sums and theta functions Abstract: The logarithmic derivative with respect to x of the Jacobi theta func tion j(x,q) involves the sum T(x,q). If N^+_{k,m}(n) equals the number of positive divisors of n that are congruent to k mod m and N^-_{k,m}(n) equals the number of negative divisors of n that are congruent to k mod m, then T(q^k,q^m)=sum_{n>0}(N^+_{k,m}(n)-N^-_{k,m}(n))q^n. An outline of a proof that T(q^k,q^m) is a theta function will be given. As defined by Dean Hickerson in his proof of the mock theta conjectures, a theta function is a finite sum of theta products times powers of q.
Last update made Tue Feb 3 16:12:29 EST 2009.
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