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On a conjecture of
Erdős and certain Dirichlet series
Tapas Chatterjee and M. Ram Murty |
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Vol. 275 (2015), No. 1, 103–113
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Abstract |
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Let f:Z∕qZ→Z be such that f(a)=±1 for 1≤a<q, and f(q)=0. Then Erdős conjectured that ∑n≥1f(n)/n≠0. For q even, it is easy to show that the conjecture is true. The case q≡3(mod4) was solved by Murty and Saradha. In this paper, we show that this conjecture is true for 82% of the remaining integers q≡1(mod4). |
Keywords
Erdős conjecture, Okada's criterion, nonvanishing of
Dirichlet series
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Mathematical Subject Classification 2010
Primary: 11M06, 11M41
Secondary: 11M20
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Milestones
Received: 20 February 2014
Revised: 5 November 2014
Accepted: 5 November 2014
Published: 12 April 2015
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Authors |
| Tapas Chatterjee | |
| Department of Mathematics Indian Institute of Technology Ropar Nangal Road Punjab 140001 India |
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| M. Ram Murty | |
| Department of Mathematics &
Statistics Queen’s University Kingston ON K7L3N6 Canada |
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