Races of irreducible monic polynomials in function fields

Abstract: Chebyshev noticed in 1853 that there is a predominance, for “most” real numbers $x ≥ 2$, of the number of primes $≤ x$ and congruent to $3$ modulo $4$ over primes $≤ x$ and congruent to $1$ modulo $4$. Since then, several generalizations of this phenomenon have been studied, notably in the case of prime number races with three or more competitors by Y. Lamzouri. In this talk, I will present results related to the generalization of Y. Lamzouri’s work in the context of polynomial rings over finite fields. I will also discuss results concerning races of irreducible monic polynomials involving two competitors. In particular, I will give examples where the races in the function field setting behave differently than in the number field setting.

Mathematics

Audience: researchers in the topic

CRG Weekly Seminars

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