Proof of a New Circle Method of Goldbach’s Conjecture

Authors

    Sheng Yao Xuelang neighborhood Guiyu Yunjian community 6-1702, China Lakeshore zone, WuXi 214000, Jiang Su, China

DOI:

https://doi.org/10.18063/lne.v3i2.760

Keywords:

New circle method, Exception module, Real zero distribution, Asymptotic formula of solution number

Abstract

In this paper, a novel circle method is introduced which, compared to previous approaches, eliminates the need to explicitly estimate the prime-variable triangle sum on the residual interval [1]. By employing the Fourier series to express the summation formula, we estimate the triangle sum on the residual interval. At the same time, the concept of the intersection set is introduced. Using this concept, we recalculate the estimated values on both the main and residual intervals, thereby forming a new circle method. This new approach focuses on proving that the main value of the solution count is equivalent to its value on the main interval. 

References

Apostol TM, 1975, Analytic Number Theory Guidance, Springer-Verlag, New York-Heidelberg.

Titchmarsh EC, 1951, The Theory of the Riemann Zeta-Function, Oxford.

Karatsuba AA, 1984, Basic Analytic Number Theory, Springer, New York.

Pan C, 1984, Goldbach Conjecture, Science Press, China.

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Published

2025-03-26