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ON ALGEBRAIC DIFFERENTIAL EQUATIONS FOR THE GAMMA FUNCTION AND $L$-FUNCTIONS IN THE EXTENDED SELBERG CLASS
Published online by Cambridge University Press: 13 March 2017
Abstract
This paper concerns the problem of algebraic differential independence of the gamma function and ${\mathcal{L}}$-functions in the extended Selberg class. We prove that the two kinds of functions cannot satisfy a class of algebraic differential equations with functional coefficients that are linked to the zeros of the ${\mathcal{L}}$-function in a domain $D:=\{z:0<\text{Re}\,z<\unicode[STIX]{x1D70E}_{0}\}$ for a positive constant $\unicode[STIX]{x1D70E}_{0}$.
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- Research Article
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- © 2017 Australian Mathematical Publishing Association Inc.
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