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In a section of his 1876 treatise Theorie der Abel'schen Functionen vom Geschlecht 3 Weber proved a formula that expresses the bitangents of a non-singular plane quartic in terms of Riemann theta constants (Thetanullwerte). The present note is devoted to a modern presentation of Weber's formula. In the end a connection with the universal bitangent matrix is also displayed.

publications mathématiques de l'université de franche-comté besançon. algèbre et théorie des nombres/publications mathématiques de besançon. algèbre et théorie des nombres

Weber’s formula for the bitangents of a smooth plane quartic