Abstract
Abstract : Hasse's conjecture over the multiplicative relations of Gaussian sums with e th power residue characters is confirmed when these sums are considered as ideals, and it is shown that the conjecture is false when these sums are considered merely as numbers. The Davenport-Hasse formula is transformed into a form analogous to the multiplication formula of the gamma function, and the Bernoulli polynomial of degree 1 defined over a cyclic group of finite order is the main tool to deal with the problem. (Author)
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