Diophantine inequality involving binary forms
Sign Up to like & getrecommendations! Published in 2017 at "Frontiers of Mathematics in China"
DOI: 10.1007/s11464-017-0602-y
Abstract: AbstractLet d ⩾ 3 be an integer, and set r = 2d−1 + 1 for 3 ⩽ d ⩽ 4, $$\tfrac{{17}} {{32}} \cdot 2^d + 1$$1732⋅2d+1 for 5 ⩽ d ⩽ 6, r = d2+d+1… read more here.
Keywords: left right; inequality involving; involving binary; diophantine inequality ... See more keywords
On generic and maximal k-ranks of binary forms
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Pure and Applied Algebra"
DOI: 10.1016/j.jpaa.2018.08.015
Abstract: In what follows, we pose two general conjectures about decompositions of homogeneous polynomials as sums of powers. The first one (suggested by G. Ottaviani) deals with the generic k-rank of comple ... read more here.
Keywords: binary forms; ranks binary; generic maximal; maximal ranks ... See more keywords
On the algebraic boundaries among typical ranks for real binary forms
Sign Up to like & getrecommendations! Published in 2018 at "Linear Algebra and its Applications"
DOI: 10.1016/j.laa.2018.07.036
Abstract: Abstract We describe the algebraic boundaries of the regions of real binary forms with fixed typical rank and of degree at most eight, showing that they are dual varieties of suitable coincident root loci. read more here.
Keywords: among typical; algebraic boundaries; boundaries among; typical ranks ... See more keywords
Representation of integers by sparse binary forms
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DOI: 10.1090/tran/8241
Abstract: We will give new upper bounds for the number of solutions to the inequalities of the shape $|F(x , y)| \leq h$, where $F(x , y)$ is a sparse binary form, with integer coefficients, and… read more here.
Keywords: number; binary forms; sparse binary; representation integers ... See more keywords