Abstract
Let F 1( x, y),…, F 2 h+1 ( x, y) be the representatives of equivalent classes of positive definite binary quadratic forms of discriminant − q ( q is a prime such that q ≡ 3 mod 4) with integer coefficients, then the number of integer solutions of F i ( x, y) = n ( i = 1,…, 2 h + 1) can be calculated for each natural number n using L-functions of imaginary quadratic field Q ((− q) 1/2).
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