Determination of the algebraic relations among special Gamma-values in positive characteristic

Abstract

We devise a new criterion for linear independence over function fields. Using this tool in the setting of dual t-motives, we find that all algebraic relations among special values of the geometric function field Gamma-function are explained by the standard functional equations.

62 pages

References in corpus (1)

• Linear independence of Gamma values in positive characteristic

Cited by in corpus (40)

• Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms
• Linear independence of monomials of multizeta values in positive characteristic
• Values of certain L-series in positive characteristic
• Multizeta values for F_q[t], their period interpretation and relations between them
• Galois theory, motives and transcendental numbers
• Expressions for values of the gamma function
• The de Rham isomorphism for Drinfeld modules over Tate algebras
• Hyperderivatives of periods and quasi-periods for Anderson $t$-modules
• tau-recurrent sequences and modular forms
• Periods of $t$-modules as special values
• Algebraic independence of periods and logarithms of Drinfeld modules (with an appendix by Brian Conrad)
• Frobenius difference equations and algebraic independence of zeta values in positive equal characteristic
• On the generalized Carlitz module
• Effective rigid analytic trivializations for Drinfeld modules
• Algebraic relations among periods and logarithms of rank 2 Drinfeld modules
• Deformation of Multiple Zeta Values and Their Logarithmic Interpretation in Positive Characteristic
• Linear relations among double zeta values in positive characteristic
• On multiple polylogarithms in characteristic $p$: $v$-adic vanishing versus $\infty$-adic Eulerianness
• Geometric Gamma values and zeta values in positive characteristic
• Analytic continuation of multiple polylogarithms in positive characteristic
• Algebraic relations among hyperderivatives of periods and logarithms of Drinfeld modules
• Algebraic independence of arithmetic gamma values and Carlitz zeta values
• On Furusho's analytic continuation of Drinfeld logarithms
• Linear equations on Drinfeld modules
• Periods of third kind for rank 2 Drinfeld modules and algebraic independence of logarithms
• Drinfeld $A$-quasi-modular forms
• On v-adic periods of t-motives
• A $t$-motivic interpretation of shuffle relations for multizeta values
• Analytic continuation of Kochubei multiple polylogarithms and its applications
• Linear relations among algebraic points on tensor powers of the Carlitz module
• Universal Families of Eulerian Multiple Zeta Values in Positive Characteristics
• Abelian equals A-finite for Anderson A-modules
• A two-variable refinement of the Stark conjecture in the function field case
• Interpolation of hypergeometric ratios in a global field of positive characteristic
• Hyperdifferential properties of Drinfeld quasi-modular forms
• Identities for Anderson generating functions for Drinfeld modules
• Signature quantization, representations of compact Lie groups, and a q-analogue of the Kostant partition function
• Complete Reducibility of t-Motives
• Interpolation of numbers of Catalan type in a local field of positive characteristic
• On finite Carlitz multiple polylogarithms