Geodesic
Refinement of the mean angle estimation in the Feyesh Toth problem
Čebyševskij sbornik, Tome 23 (2022) no. 3, pp. 245-248 Cet article a éte moissonné depuis la source Math-Net.Ru

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The Fejes Tóth problem about the maximum $E_{*}$ of the mean value of the sum of angles between lines in $\mathbb{R}^{3}$ with a common center is considered. L. Fejes Tóth suggested that $E_{*}=\frac{\pi}{3}=1.047\ldots$. This conjecture has not yet been proven. D. Bilyk and R.W. Matzke proved that $E_{*}\le 1.110\ldots$. We refine this estimate using an extremal problem of the Delsarte type: $E_{*}\le A_{*}1.08326$. Using the dual problem $B_{*}$ we show that the solution of the $A_{*}$ problem does not allow us to prove the Fejes Tóth conjecture, since $1.05210$.
Mots-clés : Fejes Tóth conjecture, Legendre polynomial
Keywords: unit sphere, linear programming bound, Delsarte problem. 
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     author = {D. V. Gorbachev and D. R. Lepetkov},
     title = {Refinement of the mean angle estimation in the {Feyesh} {Toth} problem},
     journal = {\v{C}eby\v{s}evskij sbornik},
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     year = {2022},
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D. V. Gorbachev; D. R. Lepetkov. Refinement of the mean angle estimation in the Feyesh Toth problem. Čebyševskij sbornik, Tome 23 (2022) no. 3, pp. 245-248. http://geodesic.mathdoc.fr/item/CHEB_2022_23_3_a17/

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