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Ramanujan-Fourier series and the conjecture D of Hardy and Littlewood.

Ramanujan-Fourier series and the conjecture D of Hardy and Littlewood.

Authors :
Gopalakrishna Gadiyar, H.
Padma, Ramanathan
Source :
Czechoslovak Mathematical Journal; Mar2014, Vol. 64 Issue 1, p251-267, 17p
Publication Year :
2014

Abstract

We give a heuristic proof of a conjecture of Hardy and Littlewood concerning the density of prime pairs to which twin primes and Sophie Germain primes are special cases. The method uses the Ramanujan-Fourier series for a modified von Mangoldt function and the Wiener-Khintchine theorem for arithmetical functions. The failing of the heuristic proof is due to the lack of justification of interchange of certain limits. Experimental evidence using computer calculations is provided for the plausibility of the result. We have also shown that our argument can be extended to the m-tuple conjecture of Hardy and Littlewood. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00114642
Volume :
64
Issue :
1
Database :
Complementary Index
Journal :
Czechoslovak Mathematical Journal
Publication Type :
Academic Journal
Accession number :
97444270
Full Text :
https://doi.org/10.1007/s10587-014-0098-5