On the class numbers of indefinite binary quadratic forms with discriminant~$dp^2$
    
    
  
  
  
      
      
      
        
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 18, Tome 286 (2002), pp. 40-47
    
  
  
  
  
  
    
      
      
        
      
      
      
    Voir la notice de l'article provenant de la source Math-Net.Ru
            
              			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 
$$
\mathop{{\sum}'}_{1\le n\le X}\frac1{h(d)}\sum_{2X\le p\le3X}h(dp^2)=O(X^2),
$$
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.
			
            
            
            
          
        
      @article{ZNSL_2002_286_a2,
     author = {E. P. Golubeva},
     title = {On the class numbers of indefinite binary quadratic forms with discriminant~$dp^2$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {40--47},
     publisher = {mathdoc},
     volume = {286},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_286_a2/}
}
                      
                      
                    E. P. Golubeva. On the class numbers of indefinite binary quadratic forms with discriminant~$dp^2$. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 18, Tome 286 (2002), pp. 40-47. http://geodesic.mathdoc.fr/item/ZNSL_2002_286_a2/