Geodesic
The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz
Evgeny Mukhin1 ; Vitaly Tarasov1 ; Alexander Varchenko2
1 Department of Mathematical Sciences<br/>Indiana University–Purdue University<br/>402 North Blackford St.<br/>Indianapolis, IN 46202-3216<br/>United States
2 Department of Mathematics<br/>University of North Carolina at Chapel Hill<br/>Chapel Hill, NC 27599-3250<br/>United States
Annals of mathematics, Tome 170 (2009) no. 2, pp. 863-881.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We prove the B. and M. Shapiro conjecture that if the Wronskian of a set of polynomials has real roots only, then the complex span of this set of polynomials has a basis consisting of polynomials with real coefficients. This, in particular, implies the following result:
DOI : 10.4007/annals.2009.170.863

Evgeny Mukhin 1 ; Vitaly Tarasov 1 ; Alexander Varchenko 2

1 Department of Mathematical Sciences<br/>Indiana University–Purdue University<br/>402 North Blackford St.<br/>Indianapolis, IN 46202-3216<br/>United States
2 Department of Mathematics<br/>University of North Carolina at Chapel Hill<br/>Chapel Hill, NC 27599-3250<br/>United States 
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Evgeny Mukhin; Vitaly Tarasov; Alexander Varchenko. The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz. Annals of mathematics, Tome 170 (2009) no. 2, pp. 863-881. doi : 10.4007/annals.2009.170.863. http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.170.863/

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