Vol. 69, No. 1, 1977

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Symmetries for sums of the Legendre symbol

Wells Johnson and Kevin J. Mitchell

Vol. 69 (1977), No. 1, 117–124

Symmetries are presented for sums of the Legendre symbol (a∕p) over certain subintervals of (0,p). The results follow from an elementary theorem which establishes linear relations among these sums. The list of subintervals of (0,p) for which the number of quadratic residues equals the number of non-residues is extended. Some simple applications to the determination of the class number of the imaginary. quadratic fields Q(√ −-p) are also given.

Mathematical Subject Classification
Primary: 10A20, 10A20
Received: 5 August 1976
Published: 1 March 1977
Wells Johnson
Kevin J. Mitchell