Ⅰ. INTRODUCTION AND RESULTS If （an） and （bn）, n=1, 2,…, are two sequences of positive rational integers, then, under Perron’s notation, the real irrational numbers A, B are defined by the simple continued fract...Ⅰ. INTRODUCTION AND RESULTS If （an） and （bn）, n=1, 2,…, are two sequences of positive rational integers, then, under Perron’s notation, the real irrational numbers A, B are defined by the simple continued fractions [a1, a2, a3,…] and [b1, b2, b3,…], respectively. In this note we wish to establish the following results under a slighter condition than that mentioned in Refs. [2] and [3].展开更多
1.Introduction In order to discuss the irrationality, the transcendence and the algebraic independence for p-adic numbers, the first author introduced in two previous papers [1, 2] a simple form for p-adic continued f...1.Introduction In order to discuss the irrationality, the transcendence and the algebraic independence for p-adic numbers, the first author introduced in two previous papers [1, 2] a simple form for p-adic continued fraction which is called p-adic simple continued fraction by making use of the algebraic theory of continued fraction in the real field mentioned by Schmidt, and gave a sufficient condition for certain p-adic integers which and whose sum, defference, product and quotient are all p-adic transcendental numbers.展开更多
基金Project supported by the National Natural Science Foundation of China
文摘Ⅰ. INTRODUCTION AND RESULTS If （an） and （bn）, n=1, 2,…, are two sequences of positive rational integers, then, under Perron’s notation, the real irrational numbers A, B are defined by the simple continued fractions [a1, a2, a3,…] and [b1, b2, b3,…], respectively. In this note we wish to establish the following results under a slighter condition than that mentioned in Refs. [2] and [3].
基金Project Supported by the Science Fund of the Chinese Academy of Science
文摘1.Introduction In order to discuss the irrationality, the transcendence and the algebraic independence for p-adic numbers, the first author introduced in two previous papers [1, 2] a simple form for p-adic continued fraction which is called p-adic simple continued fraction by making use of the algebraic theory of continued fraction in the real field mentioned by Schmidt, and gave a sufficient condition for certain p-adic integers which and whose sum, defference, product and quotient are all p-adic transcendental numbers.
