Rational points on the variety $n_0^3=(m_1^2+m_2^2+m_3^2+m_4^2)n$

Speaker: 翟文广 (中国矿业大学(北京))

Venue: B1044

Time: 2018年01月30日   09:00-11:00

Title: Rational points on the variety $n_0^3=(m_1^2+m_2^2+m_3^2+m_4^2)n$.

Abstract: Consider  the variety $n_0^3=(m_1^2+m_2^2+m_3^2+m_4^2)n$.  Define the height function $H(|n_0|, sqrt{m_1^2+m_2^2+m_3^2+m_4^2},|n|)$. Let $N(B)$ denote the number of rational points in the above variety such that $H(|n_0|, sqrt{m_1^2+m_2^2+m_3^2+m_4^2},|n|)leq B,  n_0not=0, nnot=0.$ We establish a new  asymptottic formula for $N(B).$