  As a continuation of previous work, we establish sum expressions for $p$-adic
Hecke $L$-functions of totally real fields in the sense of Delbourgo, assuming
a totally real analog of Heegner hypothesis. This is done by finding explicit
formulas of the periods of the corresponding $p$-adic measures. As an
application, we extend the Ferrero-Greenberg formula of derivatives of $p$-adic
$L$-functions to this setting.

Number Theory