Exploring zero free regions for fractional hypergeometric zeta functions

Hunduma Legesse Geleta ()
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Hunduma Legesse Geleta: Addis Ababa University

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 2, 467-474

Abstract: Abstract In this paper the product of classical Riemann zeta function $$\zeta (s)$$ ζ ( s ) and fractional hypergeometric zeta functions $$\zeta _a(s)$$ ζ a ( s ) is examined. As a result of this product a new integral representation of the square of the Riemann zeta function is obtained. We use this integral representation to show that some special Mellin transforms which are naturally related to the fractional hypergeometric zeta functions have zero free regions in the specified right half of the complex plane. Finally we show that the fractional hypergeometric zeta functions $$\zeta _a(s)$$ ζ a ( s ) are zero free for some specified values of a.

Keywords: Zeta function; Hypergeometric zeta functions; Fractional Hypergeometric zeta functions; Integral representation; Mellin transforms; Product formula; Uniform convergence and Absolute convergence (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00268-z

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