Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 393-404

A GENERALIZATION OF THE EICHLER TRACE FORMULA FOR MORPHISMS BETWEEN RIEMANN SURFACES

Masaharu Tanabe

Tokyo Institute of Technology, Department of Mathematics
Ohokayama, Meguro, Tokyo, 152-8551, Japan; tanabe.m.ac 'at' m.titech.ac.jp

Abstract. Let T be an automorphism of a closed Riemann surface. The Eichler trace formula asserts that the trace of the pull-back action of T on the space of holomorphic 1-forms can be evaluated in terms of the local behavior of T around the fixed points. In this paper, we will generalize this formula for morphisms between closed Riemann surfaces of possibly different genera.

2010 Mathematics Subject Classification: Primary 30F30; Secondary 14F25.

Key words: Riemann surfaces, Eichler trace formula, Lefschetz trace formula.

Reference to this article: M. Tanabe: A generalization of the Eichler trace formula for morphisms between Riemann surfaces. Ann. Acad. Sci. Fenn. Math. 42 (2017), 393-404.

Full document as PDF file

https://doi.org/10.5186/aasfm.2017.4224