Limiting Properties of the Distribution of Primes in an Arbitrarily Large Number of Residue Classes
| Autor: | Lucile Devin |
|---|---|
| Přispěvatelé: | Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Almost periodic function
Mathematics - Number Theory Logarithm General Mathematics 010102 general mathematics Prime number 0102 computer and information sciences 01 natural sciences Chebyshev filter [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] Combinatorics Arbitrarily large 010201 computation theory & mathematics Chebyshev's bias FOS: Mathematics Number Theory (math.NT) 0101 mathematics Function field Mathematics Prime number theorem |
| Zdroj: | Canadian Mathematical Bulletin Canadian Mathematical Bulletin, 2020, 63 (4), pp.837-849. ⟨10.4153/S0008439520000089⟩ |
| ISSN: | 0008-4395 |
| DOI: | 10.4153/S0008439520000089⟩ |
| Popis: | We generalize current known distribution results on Shanks–Rényi prime number races to the case where arbitrarily many residue classes are involved. Our method handles both the classical case that goes back to Chebyshev and function field analogues developed in the recent years. More precisely, let $\unicode[STIX]{x1D70B}(x;q,a)$ be the number of primes up to $x$ that are congruent to $a$ modulo $q$. For a fixed integer $q$ and distinct invertible congruence classes $a_{0},a_{1},\ldots ,a_{D}$, assuming the generalized Riemann Hypothesis and a weak version of the linear independence hypothesis, we show that the set of real $x$ for which the inequalities $\unicode[STIX]{x1D70B}(x;q,a_{0})>\unicode[STIX]{x1D70B}(x;q,a_{1})>\cdots >\unicode[STIX]{x1D70B}(x;q,a_{D})$ are simultaneously satisfied admits a logarithmic density. |
| Databáze: | OpenAIRE |
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