A variation on the theme of Nicomachus
We prove some conjectures of K. Stolarsky concerning the first and third moment of the Beatty sequences with the golden section and its square.
math.NT↗
arXiv subjects
Geremías Polanco
Publications and source records attributed to Geremías Polanco.
Continuous Distribution Arising From the Three Gaps Theorem
The well known Three Gap Theorem states that there are at most three gap sizes in the sequence of fractional parts $\{αn\}_{n<N}$ . It is known that if one averages over α, the distribution becomes continuous. We present an alternative approach, which establishes this averaged result and also provides good bounds for the error terms.
math.NT↗