Correlation of multiplicative functions over function fields

2019/05/22 by Pranendu Darbar, Darbar, Pranendu, Anirban Mukhopadhyay +1
Computer Science · Mathematics · #11T55 #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1905.09303

openalex publication_date 2019/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we study the asymptotic behaviour of the correlation functions over polynomial ring \mathbbF_q[x]. Let M_{n, q} and P_{n, q} be the set of all monic polynomials and monic irreducible polynomials of degree n over \mathbbF_q respectively. For multiplicative functions ψ₁ and ψ₂ on \mathbbF_q[x], we obtain asymptotic formula for the following correlation functions for a fixed q and n→ ∞ amp;S₂(n, q):=∑_f∈ M_{n, q}ψ₁(f+h₁) ψ₂(f+h₂),
amp;R₂(n, q):=∑_P∈ P_{n, q}ψ₁(P+h₁)ψ₂(P+h₂), where h₁, h₂ are fixed polynomials of degree

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