Periodic continued fractions and hyperelliptic curves

On the Structure of the Period of the continued fraction for $\sqrt{d}$

The paper examines the structure of the periodic continued fraction for $\sqrt{d}$ and gives formulae for the central term as well as the repeated partial quotients occurring in its period.

关于与模形式和算术函数相关的非周期连续分数的超越性

On transcendence of non-periodic continued fractions associated with modular forms and arithmetic functions

本文研究了与模形式和算术函数相关的非周期连续分数的超越性，推导了多个算术函数序列的非周期性，并构造了相应的超越数。

Symmetries of quadratic forms classes and of quadratic surds continued fractions. Part II: Classification of the periods' palindromes

The continue fractions of quadratic surds are periodic, according to a theorem by Lagrange. Their periods may have differing types of symmetries. This work relates these types of symmetries to the symmetries of the classes of the corresponding indefinite quadratic forms. This allows to classify the periods of quadratic surds and at the same time to find, for an arbitrary indefinite quadratic form, the symmetry type of its class and the number of integer points, for that class, contained in each domain of the Poincare' model of the de Sitter world, introduced in Part I. Moreover, we obtain the …