ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

3. Number Theory and Arithmetic Algebraic Geometry

1991 MS Classification: 11E76, 11M41, 11R42 Nakagawa, Jin, Joetsu University of Education Ohno conjecture on the zeta functions associated with the space of binary cubic forms The zeta functions associated with the space of binary cubic forms was defined by T. Shintani. He introduced four Dirichlet series whose coefficients are class numbers of integral binary cubic forms. Y. Ohno presented a conjecture which states that the two of the four Dirichlet series are essentially the same as the remaining two series up to some elementary factors. The proof of the conjecture and some applications will be given. Reference: J. Nakagawa, On the relations among the class numbers of binary cubic forms, to appear in invent. math.