科研之友
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摘要
We prove a version of Schanuel%26apos;s theorem in the noncommutative case : we provide an asymptotic formula for the number of one-dimensional left sub-spaces of D-N of height at most H, where D is a finite dimensional rational division algebra, N a positive integer and H a real number. The height, as considered in a previous paper, is defined with the help of a maximal order in D and a positive anti-involution. We give a completely explicit main term involving class number, regulator, discriminant and zeta function of D. We also compute an explicit error term.
- 出版日期2013
