Rocky Mountain Journal of Mathematics

On the irrationality of infinite series of reciprocals of square roots

Jaroslav Hančl and Radhakrishnan Nair

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Abstract

This paper gives sufficient conditions on the sequence $\{a_n\}_{n=1}^\infty $ of positive integers to ensure that the number $\sum _{n=1}^\infty 1/{\sqrt {a_n}}$ is irrational.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 5 (2017), 1525-1538.

Dates
First available in Project Euclid: 22 September 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1506045623

Digital Object Identifier
doi:10.1216/RMJ-2017-47-5-1525

Mathematical Reviews number (MathSciNet)
MR3705763

Zentralblatt MATH identifier
1382.11046

Subjects
Primary: 11J72: Irrationality; linear independence over a field

Keywords
Irrationality infinite series square roots

Citation

Hančl, Jaroslav; Nair, Radhakrishnan. On the irrationality of infinite series of reciprocals of square roots. Rocky Mountain J. Math. 47 (2017), no. 5, 1525--1538. doi:10.1216/RMJ-2017-47-5-1525. https://projecteuclid.org/euclid.rmjm/1506045623


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