Salvato in:
| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2101.08038 |
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Sommario:
- While the twin prime conjecture is still famously open, it holds true in the setting of finite fields: There are infinitely many pairs of monic irreducible polynomials over $\mathbb{F}_q$ that differ by a fixed constant, for each $q \geq 3$. Elementary, constructive proofs were given for different cases by Hall and Pollack. In the same spirit, we discuss the construction of a further infinite family of twin prime tuples of odd degree, and its relations to the existence of certain Wieferich primes and to arithmetic properties of the combinatorial Bell numbers.