The divisor function on residue classes I

• Autorzy: Prapanpong Pongsriiam , Robert C. Vaughan
• Języki publikacji: EN

Abstrakty

EN

Let d(n) be the number of positive divisors of n, and let $c_r(a)$ be Ramanujan's sum. We prove that for q ≥ 1, a ∈ ℤ, and x ≥ 1,
∑_{\substack{n≤ x\\ n≡ a mod q}} d(n) = x/q ∑_{r|q} (c_r(a))/r (log x/r² + 2γ - 1) +O((x^{1/3} + q^{1/2})x^{ε})$.

Kategorie tematyczne

• 11N37: Asymptotic results on arithmetic functions
• 11A25: Arithmetic functions; related numbers; inversion formulas
• 11B25: Arithmetic progressions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 168
• Numer: 4
• Strony: 369-381

Daty

wydano

2015

Twórcy

autor

Prapanpong Pongsriiam

• Department of Mathematics, Faculty of Science, Silpakorn University, Nakhon Pathom, 73000, Thailand

autor

Robert C. Vaughan

• Department of Mathematics, McAllister Building, Pennsylvania State University, University Park, PA 16802-6401, U.S.A.

Identyfikatory

DOI

10.4064/aa168-4-3