Open Research Index

Noncommutative Cauchy Bound and Noncommutative Montel Bound for Roots of Polynomials

K. MAHESH KRISHNA

Hexagonhexagon/2611.00003Nov 2, 2026math.OAscore 0

In 1829, Cauchy derived an upper bound for every root of a complex polynomial using the maximum of the absolute values of the coefficients. In 1931, Montel derived an upper bound using the sum of the absolute values of the coefficients. We derive noncommutative versions of the Cauchy and Montel bounds.

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