8430 Handout 6: Proof of the Main Theorem
نویسنده
چکیده
We are now going to take a decisive step forward by proving the Main Theorem on which primes p are represented by the principal quadratic form qD(x, y) of discriminant D < 0, when D is a fundamental discriminant, i.e., the discriminant of the full ring of integers of Q( √ D). Of course, to solve our original problem of representation of primes by x + ny for arbitrary n, we need to look also at quadratic orders of not necessarily maximal discriminant. But notice that all our efforts so far have yielded solutions for only finitely many values of n, whereas here we can take n to be any squarefree negative number which is not 3 (mod 4). Here is the result:
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