Algebraic independence of arithmetic gamma values and Carlitz zeta values
نویسندگان
چکیده
منابع مشابه
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.
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In analogy with values of the classical Euler Γ-function at rational numbers and the Riemann ζ-function at positive integers, we consider Thakur’s geometric Γ-function evaluated at rational arguments and Carlitz ζ-values at positive integers. We prove that, when considered together, all of the algebraic relations among these special values arise from the standard functional equations of the Γ-f...
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Multiple zeta values have been studied by a wide variety of methods. In this article we summarize some of the results about them that can be obtained by an algebraic approach. This involves “coding” the multiple zeta values by monomials in two noncommuting variables x and y. Multiple zeta values can then be thought of as defining a map ζ : H0 → R from a graded rational vector space H0 generated...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2010
ISSN: 0001-8708
DOI: 10.1016/j.aim.2009.09.013