Abstract
We establish a series of relations between the numbers of solutions of some positive definite ternary quadratic forms and the class numbers of the corresponding imaginary quadratic fields. In particular, we obtain an explicit formula for the ternary quadratic form , where p and q are odd primes. Let h(d) be the class number of , and for a ternary quadratic form Q, we use for the number of integral solutions (x, y, z) of the equation . We give two examples to illustrate our results: (i) For , if m is a square-free positive integer with , then(ii) for , if m is a square-free positive integer with , then
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
