5 papers
Uniform cubic bounds for irrational values of the dilogarithm
Hu Tan, Ying Zhang
We study explicit denominator conditions ensuring the irrationality of the dilogarithm at positive and negative rational points. We prove that is irratio…
A Computational Verification of the Markov Uniqueness Conjecture for
Hu Tan, Ying Zhang
We describe a finite computational verification of Markov Uniqueness Conjecture for normalized positive integer solutions of with . The archi…
Periodic Tilings of Cardinality Twice a Prime or Nine in Arbitrary Dimension
Hu Tan, Ying Zhang
We prove that every finite translational tile of of cardinality , where is an odd prime, or of cardinality nine admits a fully periodic tiling complement. The…
Fuglede's Conjecture for Cyclic Groups of Square-free Order
Hu Tan, Ying Zhang
We prove Fuglede's conjecture for finite cyclic groups of square-free order. Specifically, if \(N\) is square-free and \(A\subseteq \mathbb Z_N\) is nonempty with \(|A|=m\), then \…
A Proof of Fraenkel's Conjecture
Hu Tan, Ying Zhang
Fraenkel's conjecture asserts that a partition of the integers into at least three Beatty sequences with distinct moduli has the binary densities , normalized…