Artin symbols over imaginary quadratic fields. (English) Zbl 07873050
This paper appears to be an expository one. For an imaginary quadratic field \(K\) and a positive integer \(N\), the author explicitly describes the action of the Artin symbol \(\bigg( \frac{K_N/K}{\mathfrak{p}} \bigg)\) (where \(K_N\) is the ray class field mod \(NO_K\) and \(\mathfrak{p}\) is a prime that is coprime to \(NO_K\)) on special values of modular forms of level \(N\). He also shows how to extend the Kronecker congruence relation for the \(j\)-function to certain modular functions of higher level.
Reviewer: Balasubramanian Sury (Bangalore)
MSC:
| 11R37 | Class field theory |
| 11E12 | Quadratic forms over global rings and fields |
| 11F03 | Modular and automorphic functions |
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