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Let H denote the complex upper half-plane and let η(z) denote Dedekind’s η-function
The well-known first limit formula of Kronecker asserts that
where z = x + iy is contained in the complex upper halfplane H, C = the Euler-Mascheroni constant, and η(z) is the Dedekind eta-function defined by
Let 
be a quadratic field of discriminant d. We say that d is a prime discriminant if d is divisible by exactly one rational prime. It is classically known that the prime discriminants are given by
(p an odd prime).
