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 {{harvs|txt|last=Shintani|year=1976|authorlink=Takuro Shintani|loc=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 {{harv|Neukirch|1999|loc=p. 507}}.
References
{{refbegin}}
- {{Neukirch ANT}}
- {{Citation | last1=Shintani | first1=Takuro | title=On evaluation of zeta functions of totally real algebraic number fields at non-positive integers | mr=0427231 | year=1976 | journal=Journal of the Faculty of Science. University of Tokyo. Section IA. Mathematics | issn=0040-8980 | volume=23 | issue=2 | pages=393–417 | zbl=0349.12007 }}
- {{citation|mr=0633664|last=Shintani|first= Takuro
|chapter=A remark on zeta functions of algebraic number fields|title= Automorphic forms, representation theory and arithmetic (Bombay, 1979)|pages= 255–260
|series=Tata Inst. Fund. Res. Studies in Math.|volume= 10|publisher= Tata Inst. Fundamental Res.|place= Bombay|year= 1981|isbn=3-540-10697-9 }}
{{refend}}
External links
- [https://www.math.umass.edu/~gunnells/pictures/pictures.html Mathematical pictures] by Paul Gunnells
Category:Theorems in algebraic number theory
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