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On the Q-linear independence of the sums ∑n=1∞σk(n)/n!
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Deajim, Abdulaziz and Siksek, Samir. (2011) On the Q-linear independence of the sums ∑n=1∞σk(n)/n! Journal of Number Theory, Vol.131 (No.4). pp. 745-749. ISSN 0022-314X
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Official URL: http://dx.doi.org/10.1016/j.jnt.2010.11.009
Abstract
Let sigma(k)(n) denote the sum of the k-th powers of the positive divisors of n. Erdos and Kac conjectured that the sum alpha(k) = Sigma(infinity)(n=1) sigma(k)(n)/n! is irrational for k >= 1. This is known to be true for k = 1, 2 and 3. Fix r >= 1. In this article we give a precise criterion for 1, alpha(1), ..., alpha(r) to be Q-linearly independent, assuming a standard conjecture of Schinzel on the prime values taken by a family of polynomials. We have verified our criterion for r = 50. (C) 2011 Elsevier Inc. All rights reserved.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | Journal of Number Theory |
| Publisher: | Academic Press |
| ISSN: | 0022-314X |
| Date: | April 2011 |
| Volume: | Vol.131 |
| Number: | No.4 |
| Page Range: | pp. 745-749 |
| Identification Number: | 10.1016/j.jnt.2010.11.009 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| Funder: | Engineering and Physical Sciences Research Council (EPSRC) |
| URI: | http://wrap.warwick.ac.uk/id/eprint/41557 |
Data sourced from Thomson Reuters' Web of Knowledge
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