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An elementary proof of some character sum identities of Apostol

Published online by Cambridge University Press:  18 May 2009

Bruce C. Berndt
Bruce C. Berndt
Affiliation:
University of Illinois, Urbana, Illinois
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Let х denote a primitive character modulo k. Using two different representations for Dirichlet L-functions, Apostol [1] recently derived a representation for

involving the sums

where m is a positive integer. Furthermore, if х(r) = (r|p)the residue class character modulo the odd prime p, he derived a representation for Mm(х) involving the sums

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 14 , Issue 1 , February 1973 , pp. 50 - 53
Copyright
Copyright © Glasgow Mathematical Journal Trust 1973

References

REFERENCES

1.Apostol, T. M., Dirichlet L.-functions and character power sums, J. Number Theory 1 (1970), 223–234.Google Scholar
2.Davenport, H., Multiplicative number theory(Chicago, 1967).Google Scholar