On Diophantine approximations of Ramanujan type q-continued fractions

摘要

We shall consider arithmetical properties of the q-continued fractions K-n=1(infinity) q(sn)(S-0 + S(1)q(n) + ... + S(h)q(hn))/T-0 + T(1)q(n) + . . . + T(l)q(ln), S-i, T-i, q is an element of K, vertical bar q vertical bar(v) < 1, and some related continued fractions where v is a fixed valuation of an algebraic number field 165 and s, h, l is an element of N. In particular, we get sharp irrationality measures for certain Ramanujan, Ramanujan-Selberg, Eisenstein and Tasoev continued fractions.