... formula for the de Rham complex and obtain a first formula (11 ) which involves differential-geometric invariants (in particular, the equivariant Ray-Singer analytic torsion); these invariants areshown ... Sons, Inc., New York, 19 94. [11 ]B. H . Gross, On the periods of abelian integrals and a formula of Chowla and Selberg,Invent. Math. 45 (19 78), 19 3– 211 . [12 ]K. K¨ohler, Equivariant analytic ... (partial) Lerch ζ-functions.Using the Hurwitz formula and some combinatorics, we can translate this intoTheorems 1 and 2. In general the fixed-point formula of [13 ], like the arithmeticRiemann-Roch...