2015/05/04 by Руслан Шарипов, Ruslan Sharipov, Sharipov, Ruslan · 2 citations
Mathematics · #11D41 #11D72 #30E10 #30E15 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.NT #msc:11D41 #msc:11D72 #msc:30E10 #msc:30E15
paper · pdf · doi:10.48550/arxiv.1505.00724
AmSTeX, 17 pages, amsppt style. arXiv admin note: substantial text overlap with arXiv:1504.07161
arxiv created 2015/05/04 · openalex publication_date 2015/05/04 · arxiv updated 2015/05/05 · openalex created_date 2022/09/02 · openalex updated_date 2026/07/28
A perfect cuboid is a rectangular parallelepiped whose edges, whose face diagonals, and whose space diagonal are of integer lengths. The second cuboid conjecture specifies a subclass of perfect cuboids described by one Diophantine equation of tenth degree and claims their non-existence within this subclass. This Diophantine equation has two parameters. Previously asymptotic expansions and estimates for roots of this equation were obtained in the case where the first parameter is fixed and the other tends to infinity. In the present paper reverse asymptotic expansions and estimates are derived in the case where the second parameter is fixed and the first one tends to infinity. Their application to the perfect cuboid problem is discussed.