3 citations · 12 across the 10 of their papers we have counts for
11 papers
Markoff spectra of Hecke groups
Byungchul Cha, Dong Han Kim
We study the initial discrete parts of the Markoff spectra of Hecke groups of index . Using a digit expansion associated with geodesics and a Perron-type formula, we classi…
On the Markoff spectrum on the Hecke group of index six
Byungchul Cha, Dong Han Kim, Deokwon Sim
The discrete part of the Markoff spectrum on the Hecke group of index 6 was determined by A.~Schmidt. In this paper, we study its Markoff and Lagrange spectra after the smallest ac…
Exponential Sums by Irrationality Exponent
Byungchul Cha, Dong Han Kim
In this article, we give an asymptotic bound for the exponential sum of the Möbius function for a fixed irrational number . This exponen…
Intrinsic Diophantine approximation on circles and spheres
Byungchul Cha, Dong Han Kim
We study Lagrange spectra arising from intrinsic Diophantine approximation of circles and spheres. More precisely, we consider three circles embedded in or $\mathbb{…
Lagrange spectrum of a circle over the Eisensteinian field
Byungchul Cha, Heather Chapman, Brittany Gelb +1
We study an intrinsic Lagrange spectrum of the unit circle in the complex plane with respect to the Eisensteinian field . We prove that the minimum o…
Intrinsic Diophantine approximation on the unit circle and its Lagrange spectrum
Byungchul Cha, Dong Han Kim
Let be the Lagrange spectrum arising from intrinsic Diophantine approximation on the unit circle by its rational points. We give a complete description of…
Number theoretical properties of Romik's dynamical system
Byungchul Cha, Dong Han Kim
We study a dynamical system that was originally defined by Romik in 2008 using an old theorem of Berggren concerning Pythagorean triples. Romik's system is closely related to the F…
An Investigation on Partitions with Equal Products
Byungchul Cha, Adam Claman, Joshua Harrington +6
An ordered triple is called admissible if there exist two different multisets and such that and share the sa…
Prime number races for elliptic curves over function fields
Byungchul Cha, Daniel Fiorilli, Florent Jouve
We study the prime number race for elliptic curves over the function field of a proper, smooth and geometrically connected curve over a finite field. This constitutes a function fi…
Independence of the zeros of elliptic curve L-functions over function fields
Byungchul Cha, Daniel Fiorilli, Florent Jouve
The Linear Independence hypothesis (LI), which states roughly that the imaginary parts of the critical zeros of Dirichlet L-functions are linearly independent over the rationals, i…
The summatory function of the Möbius function in function fields
Byungchul Cha
We study the growth rate of the summatory function of the Möbius function in the context of an algebraic curve over a finite field. Our work shows a strong resemblance to its numbe…