Date: 20 May 2011

On Weierstraß semigroups at one and two points and their corresponding Poincaré series

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The aim of this paper is to introduce and investigate the Poincaré series associated with the Weierstraß semigroup of one and two rational points at a (not necessarily irreducible) non-singular projective algebraic curve defined over a finite field, as well as to describe their functional equations in the case of an affine complete intersection.

Communicated by B. Siebert.
Supported partially by the grant of the Spanish Government “Ministerio de Educación MTM2007-64704”, in cooperation with the European Union in the framework of the founds “FEDER”, by the grant of the Deutsches Akademischen Austauschdienst (DAAD)–La Caixa, and by the Deutsche Forschungsgemeinschaft (DFG).