Number Theory

    

On the Complementary Modular Symmetry Between Bernoulli Numbers with Denominator 6 and Goldbach Partitions

Authors: Chenglian Liu, Sonia Chien-I Chen, Ruopengyu Xu

This paper establishes a novel connection between two classical number theory phenomena: 1) Bernoulli numbers $B_n$ with denominator $6$ ($n equiv 2 pmod{6}$) governed by the von Staudt-Clausen theorem, and 2) the enhanced Goldbach partitions for even numbers $x equiv 0 pmod{6}$. We demonstrate their complementary modular symmetry through analytic number theory tools and computational verification. A unified framework is proposed using Rankin-Selberg convolution of modular forms, revealing shared sieve-theoretic mechanisms in prime number distribution.

Comments: 2 Pages.

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[v1] 2025-04-19 08:36:11

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