Zeros of the alternating zeta function on the line R(s)=1
| dc.creator | Sondow, Jonathan | |
| dc.date | 2002-09-27 | |
| dc.date | 2003-03-19 | |
| dc.date.accessioned | 2026-07-07T04:51:20Z | |
| dc.date.available | 2026-07-07T04:51:20Z | |
| dc.description | The alternating zeta function zeta*(s) = 1 - 2^{-s} + 3^{-s} - ... is related to the Riemann zeta function by the identity (1-2^{1-s})zeta(s) = zeta*(s). We deduce the vanishing of zeta*(s) at each nonreal zero of the factor 1-2^{1-s} without using the identity. Instead, we use a formula connecting the partial sums of the series for zeta*(s) to Riemann sums for the integral of x^{-s} from x=1 to x=2. We relate the proof to our earlier paper "The Riemann Hypothesis, simple zeros, and the asymptotic convergence degree of improper Riemann sums," Proc. Amer. Math. Soc. 126 (1998) 1311-1314. | |
| dc.description | Typo corrected after equation (4); published in Amer. Math. Monthly 110 (2003) 435-437 | |
| dc.identifier | https://arxiv.org/abs/math/0209393 | |
| dc.identifier | http://arxiv.org/abs/math/0209393 | |
| dc.identifier | Amer. Math. Monthly 110 (2003) 435-437 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65110 | |
| dc.subject | Number Theory | |
| dc.subject | 11M26 | |
| dc.title | Zeros of the alternating zeta function on the line R(s)=1 | |
| dc.type | text |