Analytic, Algebraic and Combinatorial studies on continued fractions

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Analytic studies of continued fractions are to obtain exact algebraic expressions for approximation evalucations of various Hurwitz and Tasoev continued fractions, some relations between Fibonacci-zeta functions and continued fractions, and some relations between zeta functions and Cauchy polynomials. Algebraic studies of continued fractions are to obtain independence measures of arithmetic functions and to construct Liouville numbers in non- Archimedean case. Combinatorial studies of continued fractions are to give upper bounds on cyclotomic numbers, and to discover linear recurrence relations associated with multinomial Pascal triangles. In addition, cross-studies of continued fractions are to show some relations among continued fractions, Fibonacci numbers and congruent numbers, and to discover the concept of poly Cauchy numbers and polynomials as some generalizations of Cauchy numbers, which are related with Bernoulli numbers.