Journal article
Small solutions of quadratic congruences, and character sums with binary quadratic forms
- 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(q5/8+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:
- Published
- Peer review status:
- Peer reviewed
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(Version of record, 122.4KB)
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- Publisher copy:
- 10.1112/S0025579315000364
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Funding
Bibliographic Details
- Publisher:
- Cambridge University Press Publisher's website
- Journal:
- Mathematika Journal website
- Volume:
- 62
- Issue:
- 2
- Pages:
- 551-571
- Publication date:
- 2016-02-18
- DOI:
- EISSN:
-
2041-7942
- ISSN:
-
0025-5793
- Source identifiers:
-
572240
Item Description
- Language:
- English
- Pubs id:
-
pubs:572240
- UUID:
-
uuid:1813b94b-cfd6-4a3b-8148-59433f1df5ea
- Local pid:
- pubs:572240
- Deposit date:
- 2015-11-04
Terms of use
- Copyright holder:
- University College London
- Copyright date:
- 2016
- Rights statement:
- © 2016 University College London
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