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Additive and Multiplicative Functions on Shifted Primes
Author(s) -
Hildebrand Adolf
Publication year - 1989
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-59.2.209
Subject(s) - multiplicative function , mathematics , multiplicative number theory , arithmetic function , mean value , value (mathematics) , sequence (biology) , additive function , character (mathematics) , pure mathematics , discrete mathematics , arithmetic , combinatorics , prime (order theory) , statistics , prime factor , mathematical analysis , geometry , biology , genetics
We prove several results on the behaviour of additive and multiplicative arithmetic functions on the sequence { p + 1} of shifted primes. In particular, we establish a complete analogue of the Erdös‐Wintner theorem for additive functions, and a partial analogue of Halász's mean value theorem for multiplicative functions. We also give a quantitative mean value estimate for multiplicative functions on shifted primes, and an application to character sums over shifted primes.