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Quadratic irrationals with short periods of expansion into continued fraction


We study the class number of an indefinite binary quadratic form of discriminant d based on the expansion of √d into a continued fraction and single out sequences of d for which h(d) has a lower-bound extimate. Progress is made for the conjecture on the estimate of the quantity of prime discriminants d with fixed length of period of expansion of √d. Bibliography: 15 titles.

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Dedicated to the 90th anniversary of G. M. Goluzin's birth

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 237, 1997, pp. 31–45.

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Golubeva, E.P. Quadratic irrationals with short periods of expansion into continued fraction. J Math Sci 95, 2192–2197 (1999).

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  • Quadratic Form
  • Continue Fraction
  • Class Number
  • Fixed Length
  • Binary Quadratic Form