8 papers
On the singularities of differential equations satisfied by -functions
Stéphane Fischler, Tanguy Rivoal
Let be a value, at an algebraic point, of a Siegel -function. As a special case of a very general interpolation result, we prove that there exists an -function such…
Representability of G-functions as rational functions in hypergeometric series
Thomas Dreyfus, Tanguy Rivoal
Fresán and Jossen have given a negative answer to a question of Siegel about the representability of every -function as a polynomial with algebraic coefficients in -function…
Abel's problem, Gauss and Cartier congruences over number fields
Ãric Delaygue, Tanguy Rivoal
Abel's problem consists in identifying the conditions under which the diferential equation , with an algebraic function in , possesses a non-zero algebr…
Rational approximations to values of -functions
Stéphane Fischler, Tanguy Rivoal
We solve a long standing problem in the theory of Siegel's -functions, initiated by Lang for Bessel's function in the 60's and considered in full generality by G. Chudnovs…
Zeros of -functions and of exponential polynomials defined over
Stéphane Fischler, Tanguy Rivoal
Zeros of Bessel functions play an important role in physics. They are a motivation for studying zeros of exponential polynomials defined over , and mo…
A new transcendence measure for the values of the exponential function at algebraic arguments
Stéphane Fischler, Tanguy Rivoal
Let be of degree and usual height , and let be of degree . Mahler proved in 1931 the foll…