An Arithmetic Sum Associated with the Classical Theta Function

Bruce C. Berndt, Raghavendra N. Bhat, Jeffrey L. Meyer +2

The sum $S(h,k):={\sum }_{j=1}^{k-1}(-1{)}^{j+1+[hj/k]}$ appears in the modular transformation formulae of the classical theta function ${\vartheta }_3(z)$. The double sum $S(k) := \sum_{h…