Periodic Arithmetical Functions and Gauss Sums

  • Tom M. Apostol
Part of the Undergraduate Texts in Mathematics book series (UTM)


Let k be a positive integer. An arithmetical function f is said to be periodic with period k (or periodic modulo k) if
$$f\left( {n + k} \right) = f\left( n \right)$$
for all integers n. If k is a period so is mk for any integer m > 0. The smallest positive period of f is called the fundamental period.


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Copyright information

© Springer Science+Business Media New York 1976

Authors and Affiliations

  • Tom M. Apostol
    • 1
  1. 1.Department of MathematicsCalifornia Institute of TechnologyPasadenaUSA

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