On a problem of Dinaburg and Sinai

Abstract

1. Introduetion.Let N be a sufficiently large integer.Let FN {a/b; 1 <_ a <b <-N, (a, b) 1, a and b are integers}.For any fractior a/b in FN, we can associate the minimum positive integer Xo <-b such that axo byo 1 for some integer y0 -> 1.Let al, ill, c2 and f12 be real numbers satisfying 0 < ll < 1 < 12 < i2 < 1.Then we put SN {a/b FN aN < a < flN < a2N < b < fl2N}.Dinaburg and Sinai [11 have studied the distribution of xo/b as a/b belongs to SN and N---* c.We shall improve both their results and

Locations

• Proceedings of the Japan Academy Series A Mathematical Sciences - View - PDF