%0 Journal Article
%T Ramanujan - Fourier Series and the Density of Sophie Germain Primes
%A H. Gopalkrishna Gadiyar
%A R. Padma
%J Mathematics
%D 2005
%I arXiv
%X A prime p is called Sophie Germain prime if 2p+1 is also prime. A formula for the density of such primes is given in a more general setting using a new approach. This method uses the Ramanujan-Fourier series for a modified von Mangoldt function. The proof remains heuristic as interchange of certain limits has not been justified. Experimental evidence using computer calculations is provided for the plausibility of the result.
%U http://arxiv.org/abs/math/0508639v1