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math.NT2026
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…
math.NT2025
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 exp…