Algebraic independence for values of integral curves

Algebraic Independence of Values of Elliptic Functions

Algebraic Independence of Arithmetic Gamma Values and Carlitz Zeta Values

We consider the values at proper fractions of the arithmetic gamma function and the values at positive integers of the zeta function for Fq [θ] and provide complete algebraic independence results for them.

On the Algebraic Independence of the Values of E - Functions

Algebraic Independence of Carlitz Zeta Values with Varying Constant Fields

As an analogue to special values at positive integers of the Riemann zeta function, for each constant field Fpr with fixed characteristic p we consider Carlitz zeta values ζr(n) at positive integers n. The main theorem of this paper asserts that among the families of Carlitz zeta values ∪∞ r=1 {ζr(1), ζr(2), ζr(3), . . . }, all the algebraic relations are those algebraic relations among each in...

ALGEBRAIC INDEPENDENCE OF CERTAIN FORMAL POWER SERIES (I)

We give a proof of the generalisation of Mendes-France and Van der Poorten's recent result over an arbitrary field of positive characteristic and then by extending a result of Carlitz, we shall introduce a class of algebraically independent series.