values of the Dedekind zeta function of (5) at negative integers


As an example of the http://planetmath.org/node/8064parent entry, we exhibit a few values of the Dedekind zeta function ζ(s,K) associated to the number field K=(5). The following are the first few values of ζ(1-k,K) for k2 even (ζ(1-k,K)=0 for odd k):

k ζ(1-k,K)
2 1/30
4 1/60
6 67/630
8 361/120
10 412751/1650
12 795286411/16380
14 568591843/30
16 54701427071177/4080
18 571363169189645713/35910
20 98510726938027364651/3300
22 58282448789678207092153/690
24 11364600197977872303826339891/32760
26 60097244486962154421889002337/30
28 27553534229181632149212403498558667/1740
30 179897691732312705009829008469165679351567/1074150
32 18959952687425212997198188226124948760804457/8160
34 1246857198273009466623646468891606914655865453/30
36 32613724432434114882079789497713006473885167100345949413/34545420
38 806046617423971060143933083079087480165364733020665319/30
40 256143677142597053855778958609943339670281438740737609308546491/270600
42 7744103059592598379932370402622990883812122603998003590194837592521/189630
44 2948486831915768046445018911155037347932306554653422623861453575795893/1380
46 189448047879825594335580602295205397993735968958688272066548049250586050109/1410
48 11220849734737403891785284646197712257525539376899788451604867938805644674521295667/1113840
50 7374830701193124787713243044624034212252297046043499899645907770420650321652018100351/8250
Title values of the Dedekind zeta function of (5) at negative integers
Canonical name ValuesOfTheDedekindZetaFunctionOfmathbbQsqrt5AtNegativeIntegers
Date of creation 2013-03-22 16:01:29
Last modified on 2013-03-22 16:01:29
Owner alozano (2414)
Last modified by alozano (2414)
Numerical id 5
Author alozano (2414)
Entry type Example
Classification msc 11R42
Classification msc 11M06