Estimates of the nonhomogeneous arithmetic minimum of the product of linear forms

1990 ◽  
Vol 52 (3) ◽  
pp. 3098-3109
Author(s):  
A. V. Malyshev
Keyword(s):  
Linear Forms ◽  
Arithmetic Minimum ◽  
Product Of Linear Forms

On the Product of Linear Forms

1943 ◽  
Vol 50 (3) ◽  
pp. 173 ◽  
Author(s):  
Gordon Pall
Keyword(s):  
Linear Forms ◽  
Product Of Linear Forms

A Note on the Product of Linear Forms

1944 ◽  
Vol 51 (3) ◽  
pp. 161
Author(s):  
Richard Bellman
Keyword(s):  
Linear Forms ◽  
Product Of Linear Forms

scholarly journals Equations for secant varieties of Chow varieties

2017 ◽  
Vol 27 (08) ◽  
pp. 1087-1111
Author(s):  
Yonghui Guan
Keyword(s):  
Secant Varieties ◽  
Linear Forms ◽  
Product Of Linear Forms ◽  
Chow Variety ◽  
The Ideal

The Chow variety of polynomials that decompose as a product of linear forms has been studied for more than 100 years. Finding equations in the ideal of secant varieties of Chow varieties would enable one to prove Valiant's conjecture [Formula: see text]. In this paper, I use the method of prolongation to obtain equations for secant varieties of Chow varieties as [Formula: see text]-modules.

scholarly journals On totally reducible binary forms: II.

2002 ◽  
Vol Volume 25 ◽  
Author(s):  
C Hooley
Keyword(s):  
Asymptotic Formula ◽  
Principal Result ◽  
Binary Form ◽  
Binary Forms ◽  
Linear Forms ◽  
Integer Coefficients ◽  
International Audience ◽  
Product Of Linear Forms ◽  
Positive Integers

International audience Let $f$ be a binary form of degree $l\geq3$, that is, a product of linear forms with integer coefficients. The principal result of this paper is an asymptotic formula of the shape $n^{2/l}(C(f)+O(n^{-\eta_l+\varepsilon}))$ for the number of positive integers not exceeding $n$ that are representable by $f$; here $C(f)>0$ and $\eta_l>0$.

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