57 citations · 275 across the 73 of their papers we have counts for
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math.AG2011★ 35 cited
On the Waring problem for polynomial rings
Ralf Fröberg, Giorgio Ottaviani, Boris Shapiro
In this note we discuss an analog of the classical Waring problem for C[x_0, x_1,...,x_n]. Namely, we show that a general homogeneous polynomial p \in C[x_0,x_1,...,x_n] of degree…
math.CA2011★ 57 cited
Hardy-Petrovitch-Hutchinson's problem and partial theta function
Vladimir Petrov Kostov, Boris Shapiro
In 1907 M.Petrovitch initiated the study of a class of entire functions all whose finite sections are real-rooted polynomials. An explicit description of this class in terms of the…
math.AG2011★ 4 cited
Discriminants, symmetrized graph monomials, and sums of squares
Per Alexandersson, Boris Shapiro
Motivated by the necessities of the invariant theory of binary forms J. J. Sylvester constructed in 1878 for each graph with possible multiple edges but without loops its symmetriz…