On multiplicative functions which are additive on sums of primes

DOI10.1007/s00010-012-0156-8zbMath1344.11005OpenAlexW1989453594MaRDI QIDQ372392

Paulius Šarka, Arturas Dubickas

Publication date: 7 October 2013

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00010-012-0156-8

zbMATH Keywords

multiplicative functionsprime numbersGoldbach conjecture

Mathematics Subject Classification ID

Goldbach-type theorems; other additive questions involving primes (11P32) Arithmetic functions; related numbers; inversion formulas (11A25) Other results on the distribution of values or the characterization of arithmetic functions (11N64)

Related Items (12)

On multiplicative functions with \(f(p+q+n_{0})=f(p)+f(q)+f(n_{0})\) ⋮ On \(k\)-additive uniqueness of the set of squares for multiplicative functions ⋮ On multiplicative functions additive on Goldbach-type sets ⋮ Multiplicative functions additive on generalized pentagonal numbers ⋮ Characterization of arithmetic functions that preserve the sum-of-squares operation ⋮ Additive uniqueness of PRIMES − 1 for multiplicative functions ⋮ A characterization of the identity with functional equations. II ⋮ Unnamed Item ⋮ Multiplicative functions additive on polygonal numbers ⋮ Multiplicative functions which are additive on triangular numbers ⋮ Multiplicative functions commutable with sums of squares ⋮ ON A -ADDITIVE UNIQUENESS SET FOR MULTIPLICATIVE FUNCTIONS

Cites Work

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• Verifying the Goldbach conjecture up to 4⋅10¹⁴
• Every odd number greater than $1$ is the sum of at most five primes
• A complete Vinogradov 3-primes theorem under the Riemann hypothesis
• On the Vinogradov bound in the three primes Goldbach conjecture
• On Šnirelman's constant under the Riemann hypothesis

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