Abstract
In this section we evaluate the sum
where q is a prime other than 2. It is easy to prove that G 2 = q if q≡1 (mod 4) and G 2 = -q if q ≡ 3 (mod 4), though this does not determine G completely. The computation is as follows. We have
.
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© 1980 Ann Davenport
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Davenport, H. (1980). Gauss’ Sum. In: Multiplicative Number Theory. Graduate Texts in Mathematics, vol 74. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-5927-3_2
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DOI: https://doi.org/10.1007/978-1-4757-5927-3_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-5929-7
Online ISBN: 978-1-4757-5927-3
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