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On the Qlinear independence of the sums ∑n=1∞σk(n)/n!
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Deajim, Abdulaziz and Siksek, Samir. (2011) On the Qlinear independence of the sums ∑n=1∞σk(n)/n! Journal of Number Theory, Volume 131 (Number 4). pp. 745749. ISSN 0022314X
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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 kth 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 Qlinearly 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  
Library of Congress Subject Headings (LCSH):  Linear dependence (Mathematics)  
Journal or Publication Title:  Journal of Number Theory  
Publisher:  Academic Press  
ISSN:  0022314X  
Official Date:  April 2011  
Dates: 


Volume:  Volume 131  
Number:  Number 4  
Page Range:  pp. 745749  
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)  
References:  [1] W. Bosma, J. Cannon, C. Playoust, The Magma algebra system I: The user language, J. Symbolic Comput. 24 (1997) 235–265, 

URI:  http://wrap.warwick.ac.uk/id/eprint/41557 
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