scholarly journals Class numbers of indefinite binary quadratic forms

1982 ◽  
Vol 15 (2) ◽  
pp. 229-247 ◽  
Author(s):  
Peter Sarnak
Keyword(s):  
Quadratic Forms ◽  
Class Numbers ◽  
Binary Quadratic Forms

Trace formulae and applications to class numbers

2014 ◽  
Vol 12 (6) ◽  
Author(s):  
Nicole Raulf
Keyword(s):  
Quadratic Forms ◽  
Hecke Operators ◽  
Class Numbers ◽  
Asymptotic Result ◽  
Quadratic Number ◽  
Binary Quadratic Forms ◽  
Quadratic Number Field ◽  
Ring Of Integers ◽  
Imaginary Quadratic Number ◽  
Trace Formulae

AbstractIn this paper we compute the trace formula for Hecke operators acting on automorphic forms on the hyperbolic 3-space for the group PSL2($\mathcal{O}_K $) with $\mathcal{O}_K $ being the ring of integers of an imaginary quadratic number field K of class number H K > 1. Furthermore, as a corollary we obtain an asymptotic result for class numbers of binary quadratic forms.

scholarly journals On Dirichlet series whose coefficients are class numbers of binary quadratic forms

1996 ◽  
Vol 142 ◽  
pp. 95-132 ◽  
Author(s):  
Boris A. Datskovsky
Keyword(s):  
Dirichlet Series ◽  
Quadratic Forms ◽  
Positive Definite ◽  
Equivalence Classes ◽  
Class Numbers ◽  
Definite Integral ◽  
Binary Quadratic Forms ◽  
Integral Solutions

For an integer d > 0 (resp. d < 0) let hd denote the number of Sl2(Z)-equivalence classes of primitive (resp. primitive positive-definite) integral binary quadratic forms of discriminant d. For where t and u are the smallest positive integral solutions of the equation t2 − du2 = 4 if d is a non-square and εd = 1 if d is a square.

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