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An elementary proof of the Davenport-Hasse relation. (English) Zbl 0999.11046
The author deduces the Davenport-Hasse relation [H. M. Davenport and H. Hasse, J. Reine Angew. Math. 172, 151–182 (1934; Zbl 0010.33803)] for \(\mathbb Z/p\mathbb Z\) from a congruence for Gauss periods he proved in [Acta Arith. 85, 377–388 (1998; Zbl 0912.11041)].
MSC:
11L05 Gauss and Kloosterman sums; generalizations
11R18 Cyclotomic extensions
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References:
[1] BERNDT B. C.-EVANS R. J.: Sums of Gauss, Eisenstein, Jacobi, Jacobsthal and Brewer. Illinois. J. Math. 23 (1979), 374-437. · Zbl 0393.12029
[2] DAVENPORT H.-HASSE H.: Die Nullstellen der Kongruenzzetafunktionen in gewissen zyklischen Fallen. J. Reine Angew. Math. 172 (1934), 151-182. · Zbl 0010.33803
[3] HASSE H.: Vorlesungen über Zahlentheorie. Springer-Verlag, Berlin-Göttingen-Heidelberg, 1950. · Zbl 0038.17703
[4] JAKUBEC S.: Note on the congruence of Ankeny-Artin-Chowla type modulo p2. Acta Arith. 85 (1998), 377-388. · Zbl 0912.11041
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