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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… Click to show full 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 $\unicode[STIX]{x1D70E}_{0}$ .
Keywords:
class;
extended selberg;
algebraic differential;
gamma function;
functions extended;
function
Journal Title: Bulletin of The Australian Mathematical Society
Year Published: 2017
Link to full text (if available)
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Journal Title: Bulletin of The Australian Mathematical Society
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!