Identities generated from the genus theory of real quadratic fields
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Abstract: Applying the genus theory of Gauss on the real quadratic fields, we derive identities involving quadratic forms and genus characters.
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Key words:
- genus theory /
- Kronecker symbol /
- Lambert series /
- Mellin transform /
- real quadratic field
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[1] SIEGEL C L. Lectures on Advanced Number Theory[M]. Mumbai:Tata Institute, 1961. [2] COHN H. Advanced Number Theory[M]. New York:Dover, 1980. [3] SHEN L C. On separation of quadratic forms on the imaginary quadratic field in its Hilbert class fields[J]. Proceedings of the American Mathematical Society, 2008, 136(9):3061-3067. https://www.ams.org/journals/proc/2008-136-09/S0002-9939-08-09287-3/
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