On the number of zeros of diagonal forms

Ishikawa, Tsuneo

doi:10.1090/S0025-5718-1995-1284669-4

On the number of zeros of diagonal forms
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Math. Comp. 64 (1995), 841-854 Request permission

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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