Linear independence of values of polylogarithms

DOI10.5802/jtnb.413zbMath1079.11038OpenAlexW2323085865MaRDI QIDQ558149

Tanguy Rivoal

Publication date: 30 June 2005

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_2003__15_2_551_0

zbMATH Keywords

hypergeometric functionsPolylogarithmsNesterenko's criterion

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Other Dirichlet series and zeta functions (11M41) Irrationality; linear independence over a field (11J72)

Related Items

Linear Forms in Polylogarithms ⋮ Linear independence criteria for generalized polylogarithms with distinct shifts ⋮ Unnamed Item ⋮ Linear independence of values of \(G\)-functions ⋮ A note on linear independence of polylogarithms over the rationals ⋮ Can polylogarithms at algebraic points be linearly independent? ⋮ On the linear independence of values of \(G\)-functions ⋮ Linear independence of values of \(G\)-functions. II: Outside the disk of convergence ⋮ SHIDLOVSKY’S MULTIPLICITY ESTIMATE AND IRRATIONALITY OF ZETA VALUES

Cites Work

• Unnamed Item
• On the linear independence of the values of polylogarithmic functions
• On the linear independence of numbers
• Diophantine properties of numbers related to Catalan's constant
• ON IRRATIONALITY OF THE VALUES OF THE FUNCTIONS $ F(x,s)$
• La fonction zêta de Riemann prend une infinité de valeurs irrationnelles aux entiers impairs
• Irrationality of infinitely many values of the zeta function at odd integers.