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- Title
A SURVEY OF RAMANUJAN EXPANSIONS.
- Authors
LUCHT, LUTZ G.
- Abstract
This paper summarizes the development of Ramanujan expansions of arithmetic functions since Ramanujan's paper in 1918, following Carmichael's mean-value-based concept from 1932 up to 1994. A new technique, based on the concept of related arithmetic functions, is introduced that leads to considerable extensions of preceding results on Ramanujan expansions. In particular, very short proofs of theorems for additive and multiplicative functions going far beyond previous borders are presented, and Ramanujan expansions that formerly have been considered mysterious are explained.
- Subjects
ARITHMETIC functions; NUMBER theory; MEAN value theorems; ADDITIVE functions; MULTIPLICITY (Mathematics); DIRICHLET series
- Publication
International Journal of Number Theory, 2010, Vol 6, Issue 8, p1785
- ISSN
1793-0421
- Publication type
Article
- DOI
10.1142/S1793042110003800