Prime-Weighted Interference Patterns Inspired by the Euler Product
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910032797368320 |
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| author | Takalo, Jouni J. |
| author_facet | Takalo, Jouni J. |
| contents | We study a prime-weighted oscillatory model inspired by structural aspects of the Euler product of the Riemann zeta function. The model defines finite superpositions of prime-frequency modes and exhibits zero-like crossings produced by destructive interference. We analyze how the weight exponent $x$ controls amplitude growth, slope scaling, and stability of crossings. A heuristic asymptotic argument identifies $x=\tfrac12$ as a distinguished balance regime separating high-energy and over-damped behavior. The results concern the defined model itself. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21719 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Prime-Weighted Interference Patterns Inspired by the Euler Product Takalo, Jouni J. Number Theory 11M06, 11N05, 42A38 We study a prime-weighted oscillatory model inspired by structural aspects of the Euler product of the Riemann zeta function. The model defines finite superpositions of prime-frequency modes and exhibits zero-like crossings produced by destructive interference. We analyze how the weight exponent $x$ controls amplitude growth, slope scaling, and stability of crossings. A heuristic asymptotic argument identifies $x=\tfrac12$ as a distinguished balance regime separating high-energy and over-damped behavior. The results concern the defined model itself. |
| title | Prime-Weighted Interference Patterns Inspired by the Euler Product |
| topic | Number Theory 11M06, 11N05, 42A38 |
| url | https://arxiv.org/abs/2602.21719 |