An Extension of Heilbronn's Class-Number Theorem
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DOI:
https://doi.org/10.18311/jims/1935/17380Abstract
Let h(d) denote the number of primitive classes of binary quadratic forms of negative discriminant d. Heilbronn has recently proved that
Theorem I.
h(d)→∞
as -d→∞.
By a slight modification of Heilbronn's argument I show that
Theorem II.
h(d)/2t→∞
as -d→∞,
where t is the number of different prime factors of d.