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- W3181330990 abstract "Let $a, w_1, w_2,cdotcdotcdot, w_r >0$ and $s in mathbb{C}$. We put $w= (w_1,cdotcdotcdot,w_r)$. Then the Barnes $r$-ple zeta function is defined by $zeta_r(s, w, a) = sum_{m_1=0}^{infty} cdotcdotcdot sum_{m_r=0}^{infty} 1/(a+m_1w_1+cdotcdotcdot +m_rw_r)^s$ when $sigma := Re(s)>r$. In this paper, we show that the Barnes double zeta function $zeta_2(sigma, w, a)$ has real zeros in the interval $(1,2)$ if and only if $0< a < (w_1+w_2)/2$ and the number of such zero is precisely one if $0< a< (w_1+w_2)/2$." @default.
- W3181330990 created "2021-07-19" @default.
- W3181330990 creator A5019368391 @default.
- W3181330990 date "2020-09-26" @default.
- W3181330990 modified "2023-09-27" @default.
- W3181330990 title "Real zeros of the Barnes double zeta function in the interval $(1, 2)$" @default.
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