On the intrinsic complexity of elimination theory
Journal of Complexity - Special issue: invited articles dedicated to J. F. Traub on the occasion of his 60th birthday
Complexity of Bezout's theorem V: polynomial time
Selected papers of the workshop on Continuous algorithms and complexity
Complexity of Bezout's theorem IV: probability of success; extensions
SIAM Journal on Numerical Analysis
Complexity and real computation
Complexity and real computation
Probabilistic Algorithms for Deciding Equivalence of Straight-Line Programs
Journal of the ACM (JACM)
How Lower and Upper Complexity Bounds Meet in Elimination Theory
AAECC-11 Proceedings of the 11th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Estimates on the Distribution of the Condition Number of Singular Matrices
Foundations of Computational Mathematics
On Smale's 17th Problem: A Probabilistic Positive Solution
Foundations of Computational Mathematics
Fast Linear Homotopy to Find Approximate Zeros of Polynomial Systems
Foundations of Computational Mathematics
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In these pages we compute the expectation of several functions of multi-variate complex polynomials. The common thread of all our outcomes is the basic technique used in their proofs. The used techniques combine essentially the unitary invariance of Bombieri-Weyl's Hermitian product and some elementary Integral Geometry. Using different combinations of these techniques we compute the expectation of the logarithm of the absolute value of an affine polynomial and we compute the expected value of Akatsuka Zeta Mahler's measure. As main consequences of these results and techniques, we show a probabilistic answer to question (d) in Armentano and Shub (2012) [2], concerning the complexity of one point homotopy, and an Arithmetic Poisson Formula for the multi-variate resultant. These two last statements and bounds are related to the complexity of algorithms for polynomial equation solving.