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- W2896944153 abstract "It is shown that the set $$R_{n}:=overline{{ mathfrak {R}z:eta _{n}(z)=0} }$$ contains an interval $$[ alpha _{n},b_{n}] $$ for some $$alpha _{n}<0$$ and $$0<b_{n}:=sup { mathfrak {R}z:eta _{n}(z)=0} $$ , where $$eta _{n}(z):=sum _{j=1}^{n}(-1)^{j-1}/j^{z}$$ is the $$n^{text {th}}$$ , $$n>2$$ , partial sum of the Dirichlet eta function $$eta (z):=sum _{j=1}^{infty }(-1)^{j-1}/j^{z}$$ . It means that in the strip $$[ alpha _{n},b_{n}] times mathbb {R}$$ no vertical sub-strip is zero-free for $$eta _{n}(z)$$ , $$n>2$$ . Since $$liminf _ {nrightarrow infty }b_{n}ge 1$$ , that property is, in particular, asymptotically true for the partial sums $$eta _{n}(z)$$ in the critical strip $$( 0,1) times mathbb {R}$$ ." @default.
- W2896944153 created "2018-10-26" @default.
- W2896944153 creator A5031404601 @default.
- W2896944153 date "2018-10-08" @default.
- W2896944153 modified "2023-10-18" @default.
- W2896944153 title "Density Intervals of Zeros of the Partial Sums of the Dirichlet Eta Function" @default.
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- W2896944153 doi "https://doi.org/10.1007/s00009-018-1252-3" @default.
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