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- W188068775 abstract "We investigate the possibility of generalization of the Cassel-McGettrick formula for the quintic Gauss sums. We construct a fundamental region for the fifth cyclotomic field. we describe in general the combinatoric of their geometry. The formula obtained so far satisfied a recurrence relation. The Euler relation is proved. We show how to extract canonicaly a root of unity once we have contructed the fundamental region. The numerical computation shows that a generalization of Cassels-McGettrick formula fails. One should actually attempt to modify the shape of the fundamental region to see if there is a new formula. We prove that there are new conjectures involving Gauss sums. This is actually supported by strong computation within a certain range. In the appendix we show that, there are Gauss sums which are rational intgers. we explicitely give a proof and how to find them." @default.
- W188068775 created "2016-06-24" @default.
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- W188068775 date "2004-09-14" @default.
- W188068775 modified "2023-09-27" @default.
- W188068775 title "The Quintic Gauss Sums" @default.
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- W188068775 hasPublicationYear "2004" @default.
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