Binomial Coefficients and Quadratic Fields

Zhi-Wei Sun

Binomial Coefficients and Quadratic Fields

数论 2007-05-23 v2 组合数学

作者: Zhi-Wei Sun

摘要

Let E be a real quadratic field with discriminant d and let p be an odd prime not dividing d. For \rho=1 or -1, we determine $\prod_{0<c<d, (d/c)=\rho} binomial coeff.{p-1}{\lfloor pc/d\rfloor}$ modulo p^2 in terms of Lucas numbers, the fundamental unit and the class number of E, where (d/c) is the Kronecker symbol.

关键词

prime number theory congruences and supercongruences class number of quadratic fields

引用

@article{arxiv.math/0401228,
  title  = {Binomial Coefficients and Quadratic Fields},
  author = {Zhi-Wei Sun},
  journal= {arXiv preprint arXiv:math/0401228},
  year   = {2007}
}

备注

10 pages; final version, accepted by Proc. AMS

Binomial Coefficients and Quadratic Fields

摘要

关键词

引用

备注

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