Binomial Coefficients and Quadratic Fields

Mathematics – Number Theory

Scientific paper

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10 pages; final version, accepted by Proc. AMS

Scientific paper

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 $\prod_{0binomial coeff.{p-1}{\lfloor pc/d\rfloor}$ modulo p^2 in terms of Lucas
numbers, the fundamental unit and the class number of E, where (d/c) is the
Kronecker symbol.

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