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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



On the number of zeros of diagonal forms

Author: Tsuneo Ishikawa
Journal: Math. Comp. 64 (1995), 841-854
MSC: Primary 11D79; Secondary 11T22, 11T23
MathSciNet review: 1284669
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Abstract: In this paper, we study the number of zeros of the equation $ X_1^e + X_2^e + \cdots + X_n^e \equiv 0\; \pmod p$, where $ e > 1$ is a positive integer and $ p \equiv 1\; \pmod e$ is a prime. For $ e = 5,7$, we compute the recurrence satisfied by these numbers, using the generalized Jacobi sums.

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Article copyright: © Copyright 1995 American Mathematical Society

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