- Abstract:
- Let Q(x, y, z) be an integral quadratic form with determinant coprime to some modulus q. We show that q | Q for some non-zero integer vector (x, y, z) of length O(q 5/8+ε ), for any fixed ε > 0. Without the coprimality condition on the determinant one could not necessarily achieve an exponent below 2/3. The proof uses a bound for short character sums involving binary quadratic forms, which extends a result of Chang.
- Publication status:
- Accepted
- Peer review status:
- Peer reviewed
- Version:
- Accepted Manuscript
- Publisher:
- University College London, Faculty of Mathematical and Physical Sciences, Department of Mathematics Publisher's website
- Journal:
- Mathematika: a journal of pure and applied mathematics Journal website
- Publication date:
- 2015-01-01
- EISSN:
-
2041-7942
- ISSN:
-
0025-5793
- URN:
-
uuid:1813b94b-cfd6-4a3b-8148-59433f1df5ea
- Source identifiers:
-
572240
- Local pid:
- pubs:572240
- Copyright date:
- 2015
Journal article
Small solutions of quadratic congruences, and character sums with binary quadratic forms
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