Abstract
We first encountered Gauss sums when determining the class number of quadratic fields. Expressions of this type occur in many other problems and Gauss was the first to recognize the great importance which these sums have in number theory. His attention was directed to the connection between these sums and the quadratic reciprocity law and he showed how a proof for the reciprocity law is obtained by determining the value of these sums. Today we know a number of methods of evaluating these sums. Among them there is a transcendental method, due to Cauchy, which is of particular interest since it is capable of generalization.
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© 1981 Springer Science+Business Media New York
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Hecke, E. (1981). The Law of Quadractic Reciprocity in Arbitrary Number Fields. In: Lectures on the Theory of Algebraic Numbers. Graduate Texts in Mathematics, vol 77. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4092-9_8
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DOI: https://doi.org/10.1007/978-1-4757-4092-9_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2814-6
Online ISBN: 978-1-4757-4092-9
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