On infinite-dimensional integer Hankel matrices

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Abstract


We construct a parametric family of infinite-dimensional integer Hankel matrices, each of matrices of this family has the following property: its principal submatrices are nonsingular, and the set of prime divisors of the determinants of the principal submatrices coincides with the set of all primes.


About the authors

V. P. Platonov

«Scientific Research Institute for System Analysis of the Russian Academy of Sciences»; Steklov Mathematical Institute of Russian Academy of Sciences

Author for correspondence.
Email: platonov@niisi.ras.ru

Russian Federation, 36-1, Nakhimovsky prospect, Moscow, 117218; 8, Gubkina street, Moscow, 119991

Аcademician of the Russian Academy of Sciences

M. M. Petrunin

«Scientific Research Institute for System Analysis of the Russian Academy of Sciences»

Email: petrunin@niisi.ras.ru

Russian Federation, 36-1, Nakhimovsky prospect, Moscow, 117218

References

  1. Платонов В. П. Теоретико-числовые свойства гиперэллиптических полей и проблема кручения в якобианах гиперэллиптических кривых над полем рациональных чисел // УМН. 2014. Т. 69. № 1. С. 3-38.
  2. Платонов В. П. О новых свойствах ганкелевых матриц над полем рациональных чисел // УМН. 2017. Т. 72. № 5 (437). С. 187-188.
  3. Платонов В.П., Петрунин М. М. О новых арифметических свойствах определителей ганкелевых матриц // ДАН. 2018. Т. 481. № 5. С. 484-485.

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