A class of hypertranscendental functions.
A class of hypertranscendental functions. (Short Communication).
A class of transcendental numbers having explicit g-adic and Jacobi-Perron expansions of arbitrary dimension
A criterion of irrationality.
A family of K3 surfaces and ... (3).
A generalisation of an identity of Lehmer
We prove an identity involving generalised Euler-Briggs constants, Euler's constant, and linear forms in logarithms of algebraic numbers. This generalises and gives an alternative proof of an identity of Lehmer (1975). Further, this identity facilitates the investigation of the (conjectural) transcendental nature of generalised Euler-Briggs constants. Earlier investigations of similar type by the present authors involved the interplay between additive and multiplicative characters. This in turn...
A generalization of Mahler's classification to several variables.
A lower bound for linear forms in logarithms
A note on a paper of Franklin
A note on elliptic functions and approximation by algebraic numbers of bounded degree
A note on the transcendence of infinite products
The paper deals with several criteria for the transcendence of infinite products of the form where is a positive algebraic number having a conjugate such that , and are two sequences of positive integers with some specific conditions. The proofs are based on the recent theorem of Corvaja and Zannier which relies on the Subspace Theorem (P. Corvaja, U. Zannier: On the rational approximation to the powers of an algebraic number: solution of two problems of Mahler and Mendès France, Acta...
A Note on Transcendental Power Series Mapping the Set of Rational Numbers into Itself
In this note, we prove that there is no transcendental entire function such that and , for all sufficiently large , where .
A problem of theodore S. Motzkin on the arithmetic mean
À propos de la méthode de Baker
A sharpening of the bounds for linear forms in logarithms
A sharpening of the bounds for linear forms in logarithms II
A sharpening of the bounds for linear forms in logarithms III
A trio of Bernoulli relations, their implications for the Ramanujan polynomials and the special values of the Riemann zeta function
We study the interplay between recurrences for zeta related functions at integer values, 'Minor Corner Lattice' Toeplitz determinants and integer composition based sums. Our investigations touch on functional identities due to Ramanujan and Grosswald, the transcendence of the zeta function at odd integer values, the Li Criterion for the Riemann Hypothesis and pseudo-characteristic polynomials for zeta related functions. We begin with a recent result for ζ(2s) and some seemingly new Bernoulli relations,...
A Vanishing Theorem for Power Series.
Accélération de la convergence de certaines récurrences linéaires