On the class numbers of indefinite binary quadratic forms with discriminant \(dp^2\). (English. Russian original) Zbl 1077.11029

Golubeva, E. P.

J. Math. Sci., New York 122, No. 6, 3603-3607 (2004); translation from Zap. Nauchn. Semin. POMI 286, 40-47 (2002).

Summary: A number of results on the average values of the class numbers of indefinite binary quadratic forms with discriminants divisible by a large square are proved. The main result is as follows.
Let \(d= 4n^2+1\). Then \[ \mathop{{\sum}'}_{1\leq n\leq X} \frac{1}{h(d)} \sum_{2X\leq p\leq 2X} h(dp^2)= O(X^2), \] where \(h(d)\) is the class number for the discriminant \(d\) and \(\sum'\) means that the summation is performed over the square-free \(d\) only.

MSC:

11E41

Class numbers of quadratic and Hermitian forms