Abstract
We study the distribution of the numbers of \({F_{{q^r}}}\)-rational points of hyperelliptic curves over a finite field Fq in odd characteristic. This extends the result of Kurlberg and Rudnick [4]. We also study the distribution of the number of \({F_{{q^r}}}\)-rational points and the trace of high powers of the Frobenius class of real hyperelliptic curves over a finite field Fq in even characteristic.
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