Problems on Periodic Simple Continued Fractions

AUTOR(ES)

Chowla, P.

RESUMO

Let N be a positive non-square integer and a1,a2,...,a3 be the partial denominators in the period of length s = s(N) of the continued fraction for √N. Also let ΣN = a3 - a3-1 + -... ± a1, and let h(d) be the class-number of Q(√d). Hirzebruch (unpublished) recently found the surprising theorem (which is a special case of more general results): If p is a prime≡3(4) and p > 3, then h(p) = 1 implies that Σp = 3h(-p).

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