JP Journal of Algebra, Number Theory and Applications
Volume 43, Issue 2, Pages 155 - 183
(August 2019) http://dx.doi.org/10.17654/NT043020155 |
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APPROXIMATE FUNCTIONAL EQUATION AND UPPER BOUNDS FOR THE BARNES DOUBLE ZETA-FUNCTION
Takashi Miyagawa
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Abstract: As one of the asymptotic formulas of the zeta-function, Hardy and Littlewood gave asymptotic formulas called the approximate functional equation. In this paper, we prove an approximate functional equation of the Barnes double zeta-function Also, applying this approximate functional equation and the van der Corput method, we obtain upper bounds for and with respect to t as |
Keywords and phrases: Barnes double zeta-function, approximate functional equation, Saddle point method, van der Corput method.
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