کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8895661 | 1630352 | 2018 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On common zeros of a pair of quadratic forms over a finite field
ترجمه فارسی عنوان
در صفهای رایج از جفت فرمهای درجه دوم در یک میدان
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
Let F be a finite field of characteristic distinct from 2, f and g quadratic forms over F, dimâ¡f=dimâ¡g=n. A particular case of Chevalley's theorem claims that if nâ¥5, then f and g have a common zero. We give an algorithm, which establishes whether f and g have a common zero in the case nâ¤4. The most interesting case is n=4. In particular, we show that if n=4 and detâ¡(f+tg) is a squarefree polynomial of degree different from 2, then f and g have a common zero. We investigate the orbits of pairs of 4-dimensional forms (f,g) under the action of the group GL4(F), provided f and g do not have a common zero. In particular, it turns out that for any polynomial p(t) of degree at most 4 up to the above action there exist at most two pairs (f,g) such that detâ¡(f+tg)=p(t), and the forms f, g do not have a common zero. The proofs heavily use Brumer's theorem and the Hasse-Minkowski theorem.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Finite Fields and Their Applications - Volume 51, May 2018, Pages 191-203
Journal: Finite Fields and Their Applications - Volume 51, May 2018, Pages 191-203
نویسندگان
A.S. Sivatski,