4 papers
On some periodic continued fractions along the extension over
Yoshinori Kanamura, Hyuga Yoshizaki
In 2021, Brock, Elkies, and Jordan generalized the theory of periodic continued fractions (PCFs) over to the ring of integers in a number field. In particular, they co…
On the proportions of soluble forms in some families of locally soluble binary quartic forms
Yasuhiro Ishitsuka, Yoshinori Kanamura
An integral binary quartic form is said to be locally soluble (resp. soluble) if the corresponding genus one curve has a rational point over for every place of $…
Some periodic integer continued fraction expansions of and application to the Pell equations
Yoshinori Kanamura, Hyuga Yoshizaki
Periodic integer continued fractions (PICFs) are generalization of the regular periodic continued fractions (RPCFs). It is classical that a RPCF expansion of an irrational number i…
How to calculate the proportion of everywhere locally soluble diagonal hypersurfaces
Yoshinori Kanamura, Yoshinosuke Hirakawa
In this paper, we establish a strategy for the calculation of the proportion of everywhere locally soluble diagonal hypersurfaces of of fixed degree. Our strategy…