کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5778304 | 1633767 | 2017 | 11 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A tight bound for Green's arithmetic triangle removal lemma in vector spaces
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: A tight bound for Green's arithmetic triangle removal lemma in vector spaces A tight bound for Green's arithmetic triangle removal lemma in vector spaces](/preview/png/5778304.png)
چکیده انگلیسی
We solve Green's problem, proving an essentially tight bound for Green's arithmetic triangle removal lemma in Fpn. We show that a polynomial bound holds, and further determine the best possible exponent. Namely, there is an explicit number Cp such that we may take δ=(ϵ/3)Cp, and we must have δâ¤ÏµCpâo(1). In particular, C2=1+1/(5/3âlog2â¡3)â13.239, and C3=1+1/c3 with c3=1âlogâ¡blogâ¡3, b=aâ2/3+a1/3+a4/3, and a=33â18, which gives C3â13.901. The proof uses the essentially sharp bound on multicolored sum-free sets due to work of Kleinberg-Sawin-Speyer, Norin, and Pebody, which builds on the recent breakthrough on the cap set problem by Croot-Lev-Pach, and the subsequent work by Ellenberg-Gijswijt, Blasiak-Church-Cohn-Grochow-Naslund-Sawin-Umans, and Alon.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 321, 1 December 2017, Pages 287-297
Journal: Advances in Mathematics - Volume 321, 1 December 2017, Pages 287-297
نویسندگان
Jacob Fox, László Miklós Lovász,