Elementary proofs of Berndt’s reciprocity laws

Tom M. (Mike) Apostol and Thiennu H. Vu

Vol. 98 (1982), No. 1, 17–23

DOI: 10.2140/pjm.1982.98.17

Abstract

Using analytic functional equations, Berndt derived three reciprocity laws connecting five arithmetical sums analogous to Dedekind sums. This paper gives elementary proofs of all three reciprocity laws and obtains them all from a common source, a polynomial reciprocity formula of L. Carlitz.

Mathematical Subject Classification

Primary: 10A20, 10A20

Milestones

Received: 21 January 1981

Published: 1 January 1982