A characterization of rational elements by Lüroth-type series expansions in the p-adic number field and in the field of Laurent series over a finite field
A class of transcendental numbers having explicit g-adic and Jacobi-Perron expansions of arbitrary dimension
A class of transcendental numbers with explicit g-adic expansion and the Jacobi-Perron algorithm
In this paper, we give transcendental numbers φ and ψ such that (i) both φ and ψ have explicit g-adic expansions, and simultaneously, (ii) the vector has an explicit expression in the Jacobi-Perron algorithm (cf. Theorem 1). Our results can be regarded as a higher-dimensional version of some of the results in [1]-[5] (see also [6]-[8], [10], [11]). The numbers φ and ψ have some connection with algebraic numbers with minimal polynomials x³ - kx² - lx - 1 satisfying (1.1) k ≥ l ≥0, k + l ≥ 2 (k,l...
A criterion of irrationality.
A geometric proof to Cantor's theorem and an irrationality measure for some Cantor's series.
A New Infinite Product Representation for Real Numbers.
A note on a paper of Oppenheim and Šalát concerning series of Cantor type
A note on linear recurrent Mahler numbers.
A note to the rationality of infinite series. I
À propos de la série
A theorem on irrationality of infinite series and applications
Applications of differential algebra to algebraic independence of arithmetic functions
We generalize and unify the proofs of several results on algebraic independence of arithmetic functions and Dirichlet series by using a theorem of Ax on the differential Schanuel conjecture. Along the way, we find counter-examples to some results in the literature.
Approximation of values of hypergeometric functions by restricted rationals
We compute upper and lower bounds for the approximation of hyperbolic functions at points
Arithmetic of linear forms involving odd zeta values
A general hypergeometric construction of linear forms in (odd) zeta values is presented. The construction allows to recover the records of Rhin and Viola for the irrationality measures of and , as well as to explain Rivoal’s recent result on infiniteness of irrational numbers in the set of odd zeta values, and to prove that at least one of the four numbers , , , and is irrational.
Arithmetical investigations of a certain infinite product
Arithmetical properties of the values of functions satisfying certain functional equations of Poincaré
Arithmetische Eigenschaften spezieller Heinescher Reihen.