Linear independence of values of \(G\)-functions. II: Outside the disk of convergence
DOI10.1007/s40316-020-00135-5zbMath1476.11099arXiv1811.08758OpenAlexW3019523715MaRDI QIDQ2022906
Tanguy Rivoal, Stéphane Fischler
Publication date: 30 April 2021
Published in: Annales Mathématiques du Québec (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1811.08758
Padé approximation\(G\)-functions\(G\)-operatorsShidlovsky's lemmaSiegel's linear independence criterion
Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Transcendence theory of other special functions (11J91) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Irrationality; linear independence over a field (11J72)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Arithmetic theory of \(E\)-operators
- Linear independence of values of polylogarithms
- Hypergeometric functions
- Systems of microdifferential equations. Notes and transl. by Teresa Monteiro Fernandes. Introd. by Jean-Luc Brylinski
- On the linear independence of numbers
- Transformées de Laplace des microsolutions de systèmes holonomes. (Laplace transforms of microsolutions of holonomic systems)
- Number theory IV: Transcendental numbers. Edited by A. N. Parshin, I. R. Shafarevich and R. V. Gamkrelidze. Transl. from the Russian by Neal Koblitz
- Padé approximants and balanced hypergeometric series.
- Gevrey series of arithmetic type. I: Purity and duality theorems
- Transcendental numbers. With a foreword by W. Dale Brownawell. Transl. from the Russian by Neal Koblitz
- Linear independence of values of \(G\)-functions
- Constructible sets of linear differential equations and effective rational approximations of polylogarithmic functions
- On the values of \(G\)-functions
- Multiple zeta values, Padé approximation and Vasilyev's conjecture
- Le théorème de Siegel–Shidlovsky revisité
- Équations différentielles linéaires et majorations de multiplicités
- Cyclic graphs and Apéry's theorem
- La fonction zêta de Riemann prend une infinité de valeurs irrationnelles aux entiers impairs
- On Diophantine approximations of the solutions of q-functional equations
- Microsolutions of differential operators and values of arithmetic Gevrey series
- Exceptional values of E-functions at algebraic points
- SHIDLOVSKY’S MULTIPLICITY ESTIMATE AND IRRATIONALITY OF ZETA VALUES
- Irrationality of infinitely many values of the zeta function at odd integers.