Geodesic
The dynamical motion of the zeros of the partial sums of \(e^{z}\), and its relationship to discrepancy theory
Electronic transactions on numerical analysis, Tome 30 (2008), pp. 128-143
With $\ddot $!#"$ denoting the -th partial sum of , let its zeros be denoted by {\S}\copyright $Acuteo$ showed in uDv QRXT RWV\ {\S} EUR QSRXT RWV \ddot $ddotS$5 1924 that !4 4 7 !#"87 \ddot $w$ uIv$$F QRXT RWVj 0lkm" " $bulletddot$'' s -- H#P n One of our new results shows, for any 7 with 7 , that 9 AaBi9 BiP q h 7 7 ###$dagger$###$^TM$od ^s $^TM$ EUR9 H#P 9 Sprq 0 0ctvu $ddotbullet$-- -- -- where is a positive constant, depending only on 7 . Also new in this paper is a study of the $cyclical nature$ of q 9 7 7 7 ###$dagger$###$^TM$rd , as a function of , when and . An upper bound for the approximate cycle 9 9 0 AaBi9 BiP 9 wH#P $9 ddot@ @ bullet7$ -- length, in this case, is determined in terms of . All this can be viewed in our $Interactive Supplement$, which shows " the dynamical motion of the (normalized) zeros of the partial sums of and their associated discrepancies.$
Classification : 30C15, 30E15
Keywords: partial sums of , szegacute$\Acute o$ curve, discrepancy function 1 2 
@article{ETNA_2008__30__a17,
     author = {Varga,  Richard S. and Carpenter,  Amos J. and Lewis,  Bryan W.},
     title = {The dynamical motion of the zeros of the partial sums of \(e^{z}\), and its relationship to discrepancy theory},
     journal = {Electronic transactions on numerical analysis},
     pages = {128--143},
     year = {2008},
     volume = {30},
     zbl = {1175.30010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__30__a17/}
}
TY  - JOUR
AU  - Varga,  Richard S.
AU  - Carpenter,  Amos J.
AU  - Lewis,  Bryan W.
TI  - The dynamical motion of the zeros of the partial sums of \(e^{z}\), and its relationship to discrepancy theory
JO  - Electronic transactions on numerical analysis
PY  - 2008
SP  - 128
EP  - 143
VL  - 30
UR  - http://geodesic.mathdoc.fr/item/ETNA_2008__30__a17/
LA  - en
ID  - ETNA_2008__30__a17
ER  - 
%0 Journal Article
%A Varga,  Richard S.
%A Carpenter,  Amos J.
%A Lewis,  Bryan W.
%T The dynamical motion of the zeros of the partial sums of \(e^{z}\), and its relationship to discrepancy theory
%J Electronic transactions on numerical analysis
%D 2008
%P 128-143
%V 30
%U http://geodesic.mathdoc.fr/item/ETNA_2008__30__a17/
%G en
%F ETNA_2008__30__a17
Varga,  Richard S.; Carpenter,  Amos J.; Lewis,  Bryan W. The dynamical motion of the zeros of the partial sums of \(e^{z}\), and its relationship to discrepancy theory. Electronic transactions on numerical analysis, Tome 30 (2008), pp. 128-143. http://geodesic.mathdoc.fr/item/ETNA_2008__30__a17/