# Journal of the Ramanujan Mathematical Society

Volume 35, Issue 1, March 2020 pp. 17–22.

Linear independence of certain numbers

**Authors**:
Veekesh Kumar

**Author institution:**Harish-Chandra Research Institute, HBNI, Chhatnag Road,
Jhunsi, Allahabad 211 019, India

**Summary: **
Let b ≥ 2 and D ≥ 1 be given integers and let 1≤ a1 < a2 be two
integers such that a1 a2 is not a perfect
square. In this article, in particular, we prove that the real
numbers
1, (∑ {n=1} {∞}) {1}/{ba1 n2}, and
∑ {n=1} {∞}) {1}/{ba2 n2}
are Q(√ {-D})-linearly independent.

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