On values of isotropic quadratic forms
| Autor: | Choudhuri, Manoj, Makadiya, Prashant J. |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $K$ be a locally compact non-discrete field of characteristic $p>2$ and $Q$ be a non-degenerate isotropic binary quadratic form with coefficients in $K$. We obtain asymptotic estimates for the number of solutions in the two-fold product of a discrete subring inside $K$, of the inequalities of the form $|Q(x,y)|<\delta$ for some $\delta>0$, where $| \cdot |$ is an ultrametric absolute value on $K$. The estimates are obtained in terms of continued fraction expansions of the coefficients of the quadratic form $Q$. Comment: The results in the $p$-adic set up are omitted as the $p$-adic version of Lemma $1$ may not be true, which was used in the previous version |
| Databáze: | arXiv |
| Externí odkaz: |
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