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تسجيل مستخدم جديدOn the linear independence of shifted powers
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نشر من قبل
Ignacio Garc\\'ia-Marco
تاريخ النشر
2017
مجال البحث
الهندسة المعلوماتية
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English
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We call shifted power a polynomial of the form $(x-a)^e$. The main goal of this paper is to obtain broadly applicable criteria ensuring that the elements of a finite family $F$ of shifted powers are linearly independent or, failing that, to give a lower bound on the dimension of the space of polynomials spanned by $F$. In particular, we give simple criteria ensuring that the dimension of the span of $F$ is at least $c.|F|$ for some absolute constant $c<1$. We also propose conjectures implying the linear independence of the elements of $F$. These conjectures are known to be true for the field of real numbers, but not for the field of complex numbers.
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