通过底函数的黎曼假设的塔伯安特征
数论
2024-12-17 v9
摘要
我们通过“正则算术函数”理论引入了一种新的塔伯安框架，这使我们能够通过将底函数与黎曼zeta函数的非平凡零点分布关联，建立黎曼假设的表征。从而获得黎曼假设的一种新型塔伯安等价物，扩展了古典塔伯安定理的适用范围，这些定理传统上仅限于素数定理。我们进一步揭示了与组合数论的联系，为“组合塔伯安理论”奠定了基础，突显了正则算术函数的更广泛适用性。
引用
@article{arxiv.2407.18859,
title = {A Tauberian characterization of the Riemann hypothesis through the floor function},
author = {Benoit Cloitre},
journal= {arXiv preprint arXiv:2407.18859},
year = {2024}
}
备注
36 pages. Major revisions: revised title and abstract to focus on Tauberian-floor function approach; restructured introduction with RAF framework; added combinatorial applications; streamlined presentation (reduced from 44 to 36 pages). All essential results preserved