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- W2070392455 abstract "The aim of this paper is to show that the Minakshisundaram-Pleijel zeta function Zk (s) of k-dimensional sphere Sk, k > 2 (defined in ERe(s) > k by '-'kk3) = E= [n(n + k 1)]5S with (k 1)!Pk (n) = R (n + 1, k 2)(2n + k 1) where the rising factorial R'(x, n) = x(x + 1) ... (x + n 1) is defined for real number x and n nonnegative integer) can be put in the form ____ 1 s k + 1 ( 1)! k(s) =E() ( 2 )(/ E k, jC(2s + 21 '2) 1=0 = where Bk ,j are explicitly computed. The above formula allows us to find explicitly the residue of Zk(s) at the pole s = k -n, n E N, 1 41 (~~~~k_-1~2 21 n nEN (k-)E a,-)( 2 )(/2)Bk k-2h-l1 1>0 In passing, we also obtain apparently new relations among the Stirling numbers." @default.
- W2070392455 created "2016-06-24" @default.
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- W2070392455 date "1994-04-01" @default.
- W2070392455 modified "2023-10-17" @default.
- W2070392455 title "On Minakshisundaram-Pleijel zeta functions of spheres" @default.
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- W2070392455 doi "https://doi.org/10.1090/s0002-9939-1994-1249872-9" @default.
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