On the Maillet--Baker continued fractions

Transcendental $p$-adic continued fractions

We establish a new transcendence criterion of $p$-adic continued fractions which are called Ruban continued fractions. By this result, we give explicit transcendental Ruban continued fractions with bounded $p$-adic absolute value of partial quotients. This is $p$-adic analogy of Baker's result. We also prove that $p$-adic analogy of Lagrange Theorem for Ruban continued fractions is not true.

函数域上连分数的超越性及内山定理的定量版本

Transcendence of continued fractions over function fields and a quantitative version of Uchiyama's theorem

本文在特征零的域上，改进拟周期连分数的Maillet-Baker判据，证明函数域内山定理的定量版本，给出代数幂级数异常好有理逼近的明确界，还得到收敛分母增长的上界，且证明回文连分数的二分性。