A Comparison of Sufficiency Condtions for the Goldbach and the Twin Primes Conjectures

ABSTRACT

It is generally known that
under the generalized Riemann hypothesis one could establish the twin primes
conjecture by the circle method, provided one could obtain the estimate *o *(*n*log^{-2}* n*) for the integral of the representation
function over the minor arcs. One of the new results here is that the
assumption of *GRH* can be removed. We compare this and other such
sufficiency results with similar results for the Goldbach conjecture.

Cite this paper

Mozzochi, C. (2014) A Comparison of Sufficiency Condtions for the Goldbach and the Twin Primes Conjectures.*Advances in Pure Mathematics*, **4**, 157-170. doi: 10.4236/apm.2014.45021.

Mozzochi, C. (2014) A Comparison of Sufficiency Condtions for the Goldbach and the Twin Primes Conjectures.

References

[1] Mozzochi, C.J. and Balasubramanian, R. (1978) Some Comments on Goldbach’s Conjecture. Report No. 11, Mittag-Leffler Institute.

[2] Balasubramanian, R. and Mozzochi, C.J. (1983) Siegel Zeros and the Goldbach Problem. Journal of Number Theory, 16, 311-332.

[3] Estermann, T. (1961) Introduction to Modern Prime Number Theory. Cambridge Univ. Press, London/New York.

[4] Montgomery, H.L. and Vaughan, R.C. (1973) Error Terms in Additive Prime Number Theory. Quarterly Journal of Mathematics, 24, 207-216.

[5] Hardy, G.H. and Wright, E.M. (1965) An Introduction to the Theory of Numbers. 4th Edition, Oxford University Press, London/New York.

[6] Carleson, L. (1966-1967) Sur la convergence et l'order des gradeur des somes partielles des series de Fourier. Marseille Notes.

[7] Tao, T. (2012) Heuristic Limitations of the Circle Method. Blog Post 20 May 2012, 1-11.

[1] Mozzochi, C.J. and Balasubramanian, R. (1978) Some Comments on Goldbach’s Conjecture. Report No. 11, Mittag-Leffler Institute.

[2] Balasubramanian, R. and Mozzochi, C.J. (1983) Siegel Zeros and the Goldbach Problem. Journal of Number Theory, 16, 311-332.

[3] Estermann, T. (1961) Introduction to Modern Prime Number Theory. Cambridge Univ. Press, London/New York.

[4] Montgomery, H.L. and Vaughan, R.C. (1973) Error Terms in Additive Prime Number Theory. Quarterly Journal of Mathematics, 24, 207-216.

[5] Hardy, G.H. and Wright, E.M. (1965) An Introduction to the Theory of Numbers. 4th Edition, Oxford University Press, London/New York.

[6] Carleson, L. (1966-1967) Sur la convergence et l'order des gradeur des somes partielles des series de Fourier. Marseille Notes.

[7] Tao, T. (2012) Heuristic Limitations of the Circle Method. Blog Post 20 May 2012, 1-11.