Continued Fraction Expansions of Algebraic Numbers and the Distribution of Prime Divisors
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| Formato: | Recurso digital |
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2025
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| _version_ | 1866901395656933376 |
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| author | Revista, Zen MATH, 10 |
| author_facet | Revista, Zen MATH, 10 |
| contents | This paper explores the intricate relationship between the continued fraction expansions of algebraic numbers and the distribution of prime divisors. We investigate the properties of the partial quotients in the continued fraction representations of algebraic numbers, focusing on how these quotients relate to the arithmetic structure of the numbers themselves. Furthermore, we delve into the connections between these continued fraction expansions and the distribution of prime divisors in related sequences and polynomials. Specifically, we examine the statistical behavior of the partial quotients and their impact on the frequency of prime factors. Our analysis combines classical continued fraction theory with modern techniques from analytic number theory and algebraic number theory. The research aims to provide new insights into the distribution of prime numbers and the approximation of algebraic numbers by rationals, contributing to a deeper understanding of both fields. |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17830613 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Continued Fraction Expansions of Algebraic Numbers and the Distribution of Prime Divisors Revista, Zen MATH, 10 This paper explores the intricate relationship between the continued fraction expansions of algebraic numbers and the distribution of prime divisors. We investigate the properties of the partial quotients in the continued fraction representations of algebraic numbers, focusing on how these quotients relate to the arithmetic structure of the numbers themselves. Furthermore, we delve into the connections between these continued fraction expansions and the distribution of prime divisors in related sequences and polynomials. Specifically, we examine the statistical behavior of the partial quotients and their impact on the frequency of prime factors. Our analysis combines classical continued fraction theory with modern techniques from analytic number theory and algebraic number theory. The research aims to provide new insights into the distribution of prime numbers and the approximation of algebraic numbers by rationals, contributing to a deeper understanding of both fields. |
| title | Continued Fraction Expansions of Algebraic Numbers and the Distribution of Prime Divisors |
| url | https://doi.org/10.5281/zenodo.17830613 |