Binomial Coefficients and Quadratic Fields

Zhi-Wei Sun

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Binomial Coefficients and Quadratic Fields

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arxiv math/0401228 v2 pith:GX7O5W6Z submitted 2004-01-19 math.NT math.CO

Binomial Coefficients and Quadratic Fields

Zhi-Wei Sun This is my paper

classification math.NT math.CO

keywords binomialquadraticclasscoeffcoefficientsdeterminediscriminantdividing

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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.

Binomial Coefficients and Quadratic Fields

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