On the biquadratic Gauss sum
- 1 January 1972
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 71 (1) , 79-83
- https://doi.org/10.1017/s0305004100050301
Abstract
1. Professor J. W. S. Cassels (in (l)) recently enunciated a conjecture concerning Kummer sums. His conjecture suggests that there is a close connexion between the Kummer sum and a certain product of Weierstrass elliptic functions.In this paper we consider the biquadratic Gauss sum. A theory similar to that used in (1) and in (4) suggests that there is a corresponding connexion between the biquadratic sum and a product of Jacobian elliptic functions. The enunciation of this conjecture appears in section 6. But first of all we require some preliminary results.Keywords
This publication has 2 references indexed in Scilit:
- On Kummer SumsProceedings of the London Mathematical Society, 1970
- Some arithmetical applications of an elliptic function.Journal für die reine und angewandte Mathematik (Crelles Journal), 1964