Shintani's unit theorem

Short description: On subgroups of finite index of the totally positive units of a number field

In mathematics, Shintani's unit theorem introduced by Shintani (1976, proposition 4) is a refinement of Dirichlet's unit theorem and states that a subgroup of finite index of the totally positive units of a number field has a fundamental domain given by a rational polyhedric cone in the Minkowski space of the field (Neukirch 1999).

References

• Neukirch, Jürgen (1999). Algebraic Number Theory. Grundlehren der mathematischen Wissenschaften. 322. Berlin: Springer-Verlag. ISBN 978-3-540-65399-8. 
• Shintani, Takuro (1976), "On evaluation of zeta functions of totally real algebraic number fields at non-positive integers", Journal of the Faculty of Science. University of Tokyo. Section IA. Mathematics 23 (2): 393–417, ISSN 0040-8980 
• Shintani, Takuro (1981), "A remark on zeta functions of algebraic number fields", Automorphic forms, representation theory and arithmetic (Bombay, 1979), Tata Inst. Fund. Res. Studies in Math., 10, Bombay: Tata Inst. Fundamental Res., pp. 255–260, ISBN 3-540-10697-9 

External links

• Mathematical pictures by Paul Gunnells