Geodesic
On the values of the Epstein zeta function
Glasgow mathematical journal, Tome 14 (1973) no. 1, pp. 1-12

Voir la notice de l'article provenant de la source Cambridge University Press

Let ζ(s) = σn-s (Res >1) denote the Riemann zeta function; then, as is well known, , where Bm denotes the mth Bernoulli number, In this paper we investigate the possibility of similar evaluations of the Epstein zeta function ζq(s) at the rational integers s = k> 2. Letbe a positive definite quadratic form andwhere the summation is over all pairs of integers except (0, 0). In attempting to evaluate ζq(k) we are guided by Kronecker's first limit formula [11]where γ is Euler's constant,is the Dedekind eta-function, and τ is the complex number in the upper half plane, H, associated with Q by the formulaOn the basis of (1.3) we would expect a formula involving functions of τ. This formula is stated in Theorem 1, (2.13). 
Smart, John Roderick. On the values of the Epstein zeta function. Glasgow mathematical journal, Tome 14 (1973) no. 1, pp. 1-12. doi: 10.1017/S001708950000166X
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