Linear independence of Gamma values in positive characteristic

Abstract

We investigate the arithmetic nature of special values of Thakur's function field Gamma function at rational points. Our main result is that all linear independence relations over the field of algebraic functions are consequences of the known relations of Anderson and Thakur arising from the functional equations of the Gamma function.

51 pages

Cited by in corpus (9)

• Determination of the algebraic relations among special Gamma-values in positive characteristic
• A Weil-Barsotti formula for Drinfeld modules
• The de Rham isomorphism for Drinfeld modules over Tate algebras
• Local Shtukas, Hodge-Pink Structures and Galois Representations
• Hyperderivatives of periods and quasi-periods for Anderson $t$-modules
• Effective rigid analytic trivializations for Drinfeld modules
• Algebraic relations among hyperderivatives of periods and logarithms of Drinfeld modules
• Periods of third kind for rank 2 Drinfeld modules and algebraic independence of logarithms
• Complete Reducibility of t-Motives