Publications of (and about) Paul Erdös
Autor: Erdös, Pál
Title: A note on Farey series. (In English)
Source: Q. J. Math., Oxf. Ser. 14, 82-85 (1943).
Review: Suppose a1/b1, a2/b2,... are the positive reduced fractions of denominator \leq n. The A. proves the existence of an absolute constant c such that if n > ck then (a\nu-a\nu+k) (b\nu-b\nu+k) \geq 0 for \nu = 1,2,... This is more specific form of a result of A.E.Mayer [same journal 13, 185-192 (1942; Zbl 061.06703)].
Classif.: * 11B57 Farey sequences; the sequences
Index Words: series, summability
© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag