Geodesic
Notes on two lemmas concerning the Epstein zeta-function
Glasgow mathematical journal, Tome 6 (1964) no. 4, pp. 202-204

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

1. We use Cassels's notation and define h (m, n), Q (m, n), Zh (s), Zh (1) – ZQ (1) and G (x, y) as in [1]. Rankin [5] proved that the Epstein zeta-function Zh (s) satisfies, for s ≧ 1·035, theTHEOREM. For s > 0, Zh (s) — ZQ (s) ≧ 0 with equality if and only ifh is equivalent to Q. Rankin then asked whether the theorem is true for all s > 1. Cassels [1] answered this question in the affirmative and proved further that the theorem is true for all s > 0. 
Diananda, P. H. Notes on two lemmas concerning the Epstein zeta-function. Glasgow mathematical journal, Tome 6 (1964) no. 4, pp. 202-204. doi: 10.1017/S2040618500035036
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[1] 1.Cassels, J. W. S., On a problem of Rankin about the Epstein zeta-function, Proc. Glasgow Math. Assoc. 4 (1959), 73–80. Google Scholar | DOI

[2] 2.Cassels, J. W. S., Corrigendum to [1], Proc. Glasgow Math. Assoc. 6 (1963), 116. Google Scholar

[3] 3.Emersleben, O., Review of [1], Zbl. Math. Google Scholar

[4] 4.Ennola, Veikko, A lemma about the Epstein zeta-function, Proc. Glasgow Math. Assoc. 6 (1964), 198–201. Google Scholar | DOI

[5] 5.Rankin, R. A., A minimum problem for the Epstein zeta-function, Proc. Glasgow Math. Assoc. 1 (1953), 149–158. Google Scholar | DOI

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