# values of the Dedekind zeta function of $\mathbb{Q}(\sqrt{5})$ at negative integers

As an example of the http://planetmath.org/node/8064parent entry, we exhibit a few values of the Dedekind zeta function $\zeta(s,K)$ associated to the number field $K=\mathbb{Q}(\sqrt{5})$. The following are the first few values of $\zeta(1-k,K)$ for $k\geq 2$ even ($\zeta(1-k,K)=0$ for odd $k$):

$k$ $\zeta(1-k,K)$
$2$ $1/30$
$4$ $1/60$
$6$ $67/630$
$8$ $361/120$
$10$ $412751/1650$
$12$ $795286411/16380$
$14$ $568591843/30$
$16$ $54701427071177/4080$
$18$ $571363169189645713/35910$
$20$ $98510726938027364651/3300$
$22$ $58282448789678207092153/690$
$24$ $11364600197977872303826339891/32760$
$26$ $60097244486962154421889002337/30$
$28$ $27553534229181632149212403498558667/1740$
$30$ $179897691732312705009829008469165679351567/1074150$
$32$ $18959952687425212997198188226124948760804457/8160$
$34$ $1246857198273009466623646468891606914655865453/30$
$36$ $32613724432434114882079789497713006473885167100345949413/34545420$
$38$ $806046617423971060143933083079087480165364733020665319/30$
$40$ $256143677142597053855778958609943339670281438740737609308546491/270600$
$42$ $7744103059592598379932370402622990883812122603998003590194837592521/189630$
$44$ $2948486831915768046445018911155037347932306554653422623861453575795893/1380$
$46$ $189448047879825594335580602295205397993735968958688272066548049250586050109/1410$
$48$ $112208497347374038917852846461977122575255393768997884516048679388056446745212% 95667/1113840$
$50$ $737483070119312478771324304462403421225229704604349989964590777042065032165201% 8100351/8250$
Title values of the Dedekind zeta function of $\mathbb{Q}(\sqrt{5})$ at negative integers ValuesOfTheDedekindZetaFunctionOfmathbbQsqrt5AtNegativeIntegers 2013-03-22 16:01:29 2013-03-22 16:01:29 alozano (2414) alozano (2414) 5 alozano (2414) Example msc 11R42 msc 11M06