Generalized continued fractions and estimates of Weyl sums and the remainder term in the distribution law for the fractional parts of the values of a polynomial
It is well-known that by continued fractions one can approximate real numbers by rationals with arbitrary accuracy. In this summary note the author states six theorems on generalized continued fractions which deal with vectors in \(n\)-dimensional space and can be applied to classical problems in analysis and number theory. Clear enough statements of all the results need rather lengthy definitions and hence are not suitable to mention here. There are no proofs of the results provided in the paper. The author remarks that some proofs need essentially his recent work in [Russ. Math. Surv. 48, 143-179 (1993); translation from Usp. Mat. Nauk 48, 131-166 (1993; Zbl 0821.11039) and Ergodic Theory Dyn. Syst. 11, 515-534 (1991; Zbl 0748.11038)].
scientific article; zbMATH DE number 830783
scientific article