6 papers
Multiplicative dependence in the sumset of multiplicative groups
Yuri Bilu, Florian Luca
Let and be finitely generated multiplicative groups of algebraic numbers such that is a finite group. We show that, up to finitely many exceptions, non-zero su…
Values of algebraic functions at Liouville numbers
Yuri Bilu, Diego Marques
In 1953 LeVeque proved the existence of -numbers by showing that for some specially defined Liouville number , the th root is in . In this article we st…
Some explicit values of a -multiple zeta function whose denominator power is not uniform
Yuri Bilu, Hideaki Ishikawa, Takao Komatsu
One of the generalizations of multiple zeta values is the -version, and in the case of finite sums, they may be expressed explicitly in polynomial form. Several results have bee…
Values of generalized Liouville power series at algebraic numbers
Yu. Bilu, D. Marques, C. G. Moreira
For every positive integer LeVeque (1953) defined the -numbers as the transcendental numbers that admit very good approximation by algebraic numbers of degree , but not…
Effective multiplicative independence of 3 singular moduli
Yuri Bilu, Sanoli Gun, Emanuele Tron
Pila and Tsimerman proved in 2017 that for every there exists at most finitely many -tuples of distinct non-zero singular moduli with the property "$x_1,…
Skolem Problem for Linear Recurrence Sequences with 4 Dominant Roots (after Mignotte, Shorey, Tijdeman, Vereshchagin and Bacik)
Yuri Bilu
It is an exposition of the work of Mignotte, Shorey, Tijdeman, Vereshchagin and Bacik on decidability of the vanishing problem for linear recurrence sequences of order 4.