A continued fraction expansion for a -tangent function.
A continued fraction expansion for a -tangent function: an elementary proof.
A continued fraction of order twelve
In this paper, we establish several explicit evaluations, reciprocity theorems and integral representations for a continued fraction of order twelve which are analogues to Rogers-Ramanujan’s continued fraction and Ramanujan’s cubic continued fraction.
A criterion for periodicity of multi-continued fraction expansion of multi-formal Laurent series
A density result for elliptic Dedekind sums
A generalization of a theorem of Euler for regular chains of complex quadratic irrationalities
A generalization of a theorem of Lekkerkerker to Ostrowski's decomposition of natural numbers
A geometric method for the approximation by nearest integer continued fractions. (Eine geometrische Methode bei der Approximation durch Kettenbrüche nach dem nächsten Ganzen.)
A localization theorem in the theory of diophantine approximation and an application to Pell's equation
A new class of continued fraction expansions
A note on rational surgeries on a Hopf link
It is clear that every rational surgery on a Hopf link in -sphere is a lens space surgery. In this note we give an explicit computation which lens space is a resulting manifold. The main tool we use is the calculus of continued fractions. As a corollary, we recover the (well-known) result on the criterion for when rational surgery on a Hopf link gives the -sphere.
A note on the Diophantine equation .
A proof of the continued fraction expansion of .
A recovery of Brouncker's proof for the quadrature continued fraction.
350 years ago in Spring of 1655 Sir William Brouncker on a request by John Wallis obtained a beautiful continued fraction for 4/π. Brouncker never published his proof. Many sources on the history of Mathematics claim that this proof was lost forever. In this paper we recover the original proof from Wallis' remarks presented in his Arithmetica Infinitorum. We show that Brouncker's and Wallis' formulas can be extended to MacLaurin's sinusoidal spirals via related Euler's products. We derive Ramanujan's...
A Schinzel theorem on continued fractions in function fields
A simple criterion for solvability of both and .
Abschätzung der Periodenlänge einer verallgemeinerten Kettenbruchentwicklung.
Allgemeine Theorie der kettenbruchähnlichen Algorithmen, in welchen jede Zahl aus drei vorhergehenden gebildet wird.
An infinite product with bounded partial quotients
Anzahl der Zerlegungen einer ganzen rationalen Zahl in Summanden