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Let $Q(x,y) = ax^2+b xy + cy^2$ be a primitive integral positive-definite quadratic form, with associated number field $K$. If $D=b^2-4ac$ is a fundamental discriminant, then it's well-known that $$\...

Let $F/ \mathbb{Q}$ be a biquadratic field of Galois group $C_2 \times C_2$. Then I know that the Dedekind Zeta function of $F$ can be factored into $L$-functions as; $$\zeta_F(s) = \zeta(s) L(s, \...

There is a generalization of the Kummer congruences to totally real number fields with characters due to Deligne-Ribet. For example, see the exposition here, more precisely see Theorem 2.1. What is ...