2019
Том 71
№ 10

All Issues

Kolmakova L. N.

Articles: 2
Article (Russian)

Exponents of elements of a normal basis of the ideal of algebraic functions on a three-sheeted Riemannian surface

Kolmakova L. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1995. - 47, № 8. - pp. 1029–1037

On a three-sheeted Riemannian surfaceR of genus ρ given by an irreducible algebraic equation, we construct normal bases of the ideal of algebraic functions that are multiples of some integer divisors. A method for constructing such normal bases was given in [V. E. Kruglov,Dokl. Akad. Nauk SSSR,321, No. 1, 11–13 (1991)]. The relations obtained for the exponents of the constructed elements enable one to determine the number of solutions of the Riemann problem for any integer divisor and to find partial indices in the problems of factorization of matrices of permutation type.

Article (Ukrainian)

A singular integral equation with a multiple-valued kernel on a hyperelliptic Riemann surface

Kolmakova L. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1985. - 37, № 5. - pp. 581–575