Document Type
Article
Publication Date
7-6-2025
Publisher
Springer Nature
Abstract
Given two irreducible conics C and D over a finite field 𝔽q with q odd, we show that there are q2/ 4 + O(q3/2) points P in P2(𝔽q) such that P is external to C and internal to D. This answers a question of Korchmáros. We also prove the analogous result for higher-dimensional smooth quadric hypersurfaces in Pn-1 with n odd, where the answer is qn-1/4 + O(qn-3/2).
Recommended Citation
Asgarli, S., & Yip, C. H. (2025). Mutual position of two smooth quadrics over finite fields. Designs, Codes and Cryptography, 93(10), 4461–4472. https://doi.org/10.1007/s10623-025-01687-9
Comments
Open access to this article is funded by Santa Clara University Library.
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