Published April 30, 2026
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Study and Consequences of the β Function on the Riemann Hypothesis
Authors/Creators
- 1. 9 allΓ©e Capitaine Jean Bernard Bossu, Talant (Bourgogne), France.
Description
Abstract : I will study the Sghiar's function β: (πΏ, π) βΌ ∏ π π− πΏ ππ π∈π , π the set of prime numbers. Which is an extension of the Riemann zeta function. The classical form of the Riemann zeta function and its Euler product are well known in analytic number theory [1], and I will showthat : π»(π) = π πππ πΉπ(π) > π π ⇒ β = π. We deduce the proof of the Riemann Hypothesis. MSC code: 11M26 ; 97F60 ; 32A10
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Additional details
Identifiers
- DOI
- 10.54105/ijam.A1231.06010426
- EISSN
- 2582-8932
Dates
- Accepted
-
2026-04-15Manuscript received on 22 December 2025 | First Revised Manuscript received on 31 December 2025 | Second Revised Manuscript received on 18 March 2026 | Manuscript Accepted on 15 April 2026 | Manuscript published on 30 April 2026.
References
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- K. Soundararajan, Moments of the Riemann zeta function, Annals of Mathematics, 2017, DOI: http://doi.org/10.4007/annals.2017.185.2.3
- A. Harper, Bounds on the Riemann zeta function, Proceedings of the London Mathematical Society, 2019, DOI: http://doi.org/10.1112/plms.12225
- M. RadziwiΕΕ and K. Soundararajan, Moments and distribution of central L-values, Inventiones Mathematicae, 2020, DOI: http://doi.org/10.1007/s00222-020-00950-6
- P. Sarnak, Three lectures on the MΓΆbius function randomness, 2021, Available at: https://publications.ias.edu/sarnak/paper/563
- E. M. Stein and R. Shakarchi, Complex Analysis, Princeton University Press. Published : Apr 27, 2003 .https://press.princeton.edu/books/hardcover/9780691113852/complexanalysis