Abstract
A new local-global result about the primitive representations of zero by integral ternary quadratic forms is proven. By an extension of a result of Kneser (given in the Appendix), it yields a quantitative supplement to the Hasse principle on the number of automorphic orbits of primitive zeros of a genus of forms. One ingredient in its proof is an asymptotic formula for a count of the zeros of a given form in such an orbit.
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Acknowledgements
I want to thank Peter Sarnak for sharing valuable insights on the general subject of this paper and also for some helpful specific comments. In addition, I am very grateful to the referee for carefully reading the paper and for suggesting numerous improvements.
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To Peter Sarnak, on the occasion of his seventieth birthday
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Duke, W., Schulze-Pillot, R. On the analytic theory of isotropic ternary quadratic forms. JAMA 151, 115–137 (2023). https://doi.org/10.1007/s11854-023-0324-x
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DOI: https://doi.org/10.1007/s11854-023-0324-x