\contentsline {section}{\numberline {1}The circle pairing}{2} \contentsline {section}{\numberline {2}Derived periods}{5} \contentsline {section}{\numberline {3}The conjecture}{12} \contentsline {section}{\numberline {4}Numerical evidence}{15} \contentsline {section}{\numberline {5}A Gross-Kohnen-Zagier formula}{18}