Michael Somos on Mon, 15 Nov 1999 19:42:39 -0500 (EST)

 more zeta() faults

```What is think is interesting is the variety of different faults encountered :

GP/PARI CALCULATOR Version 2.0.18 (development)
i686 running linux (ix86 kernel) 32-bit version
(readline v2.2 enabled, extended help available)
..
parisize = 4000000, primelimit = 500000
gp> for(n=1,30,print(n" "zeta(I+10^n)))
1 1.000759077829856768809901195 - 0.0006401280267855239745764942372*I
2 1.000000000000000000000000000 - 2.623314226356272336124975847 E-31*I
3 1.000000000000000000000000000 - 2.993549263496598102783842505 E-302*I
4 1.000000000000000000000000000 - 1.601996728198064104058581242 E-3011*I
5 1.000000000000000000000000000 - 3.198125608525491241840590787 E-30104*I
6 1.000000000000000000000000000 - 3.226876165408552144077256540 E-301031*I
***   overflow in R*R
gp> for(n=1,30,print(n" "zeta(0+10^n)))
1 1.000994575127818085337145958
2 1.000000000000000000000000000
3 1.000000000000000000000000000
4 1.000000000000000000000000000
5 1.000000000000000000000000000
6 1.000000000000000000000000000
7 1.000000000000000000000000000
8 1.000000000000000000000000000
9 1.000000000000000000000000000
***   impossible assignment I-->S
gp> for(n=1,30,print(n" "zeta(1/3*10^n)))
1 1.147356236882742872645615288
2 1.000000000092399026901528289
3 1.000000000000000000000000000
4 1.000000000000000000000000000
5 1.000000000000000000000000000
6 1.000000000000000000000000000
7 1.000000000000000000000000000
***   exponent too large in exp.
gp> for(n=1,10,print(n" "zeta(1/10000^n)))
1 -0.5000919038861036320095103010
2 -0.5000000091893854323645512140
3 -0.5000000000009189385332056772
4 -0.5000000000000000918938718545
5 -0.5000000000000000000748188871
6 -0.5000000000000005856439856969
7 -0.5000000000070312676220292861
8 -0.5000001009959118357014707048
9 -0.5013897738467078603232921279
10 -18.70857365099656195236164656

Sorry to bear bad news. Shalom, Michael
```