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Around the 'Fundamental Theorem of Algebra' (extended version)
Boris Kazarnovskii
The Fundamental Theorem of Algebra (FTA) asserts that every complex polynomial has as many complex roots, counted with multiplicities, as its degree. A probabilistic analogue of th…
Around the "Fundamental Theorem of Algebra"
Boris Kazarnovskii
The Fundamental Theorem of Algebra (FTA) asserts that every complex polynomial has as many complex roots, counted with multiplicities, as its degree. A probabilistic analogue of th…
On the exponential algebraic geometry
B. Kazarnovskii
The set of roots of any finite system of exponential sums in the space is called an exponential variety. We define the intersection index of varieties of complementa…
The zeros of random sections of real vector bundles
Boris Kazarnovskii
We define integral geometric analogues of the Chern classes for real vector bundle on a smooth real variety. More precisely, we define the Chern densities of a real bundle. These d…
How many roots of a system of random trigonometric polynomials are real?
Boris Kazarnovskii
The expected number of zeros of a random real polynomial of degree asymptotically equals . On the other hand, the average fraction of real zeros of a random tr…