An analogue of Ramanujan%26apos;s sum with respect to regular integers (modr)

作者：Haukkanen Pentti^*; Toth Laszlo

来源：Ramanujan Journal, 2012, 27(1): 71-88.

DOI：10.1007/s11139-011-9327-9

• Ramanujan%26apos
• s sum
• Regular integer
• Arithmetical convolution
• Even function
• Discrete Fourier transform
• Multiplicative function
• Mean value
• Dirichlet series

An integer a is said to be regular (modr) if there exists an integer x such that a (2) xa parts per thousand a (mod r). In this paper we introduce an analogue of Ramanujan%26apos;s sum with respect to regular integers (modr) and show that this analogue possesses properties similar to those of the usual Ramanujan%26apos;s sum.

• 出版日期2012-1