Geodesic
Prym Differentials on a~Finite Riemann Surface
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 3, pp. 335-347.

Voir la notice de l'article provenant de la source Math-Net.Ru

V. V. Chueshev has constructed a general theory of multiplicative (multi-valued) functions and Prym differentials on a compact Riemann surface. In this article we begin to construct the theory of Prym differentials on a finite Riemann surface. Explicit forms of all elementary Prym differentials for every characters are given. We find the dimensions of two important factor spaces of Prym differentials and the dimension of the first holomorphic de Rham cohomology group of Prym differentials for unessential characters. Moreover we give explicit bases in these factor spaces. We also give formulae for multiplicative functions and multiplicative units for every characters on finite Riemann surfaces.
Keywords: multiplicative function, Prym differential. 
@article{JSFU_2008_1_3_a13,
     author = {Anna N. Chichkakova and Viktor V. Chueshev},
     title = {Prym {Differentials} on {a~Finite} {Riemann} {Surface}},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {335--347},
     publisher = {mathdoc},
     volume = {1},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2008_1_3_a13/}
}
TY  - JOUR
AU  - Anna N. Chichkakova
AU  - Viktor V. Chueshev
TI  - Prym Differentials on a~Finite Riemann Surface
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2008
SP  - 335
EP  - 347
VL  - 1
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2008_1_3_a13/
LA  - ru
ID  - JSFU_2008_1_3_a13
ER  - 
%0 Journal Article
%A Anna N. Chichkakova
%A Viktor V. Chueshev
%T Prym Differentials on a~Finite Riemann Surface
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2008
%P 335-347
%V 1
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2008_1_3_a13/
%G ru
%F JSFU_2008_1_3_a13
Anna N. Chichkakova; Viktor V. Chueshev. Prym Differentials on a~Finite Riemann Surface. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 3, pp. 335-347. http://geodesic.mathdoc.fr/item/JSFU_2008_1_3_a13/

[1] V. V. Chueshev, Multiplikativnye funktsii i differentsialy Prima na peremennoi kompaktnoi rimanovoi poverkhnosti, Chast 2, KemGU, Kemerovo, 2003 | Zbl

[2] H. M. Farkas, I. Kra, Riemann Surfaces, Graduate Texts in Mathematics, 71, Springer-Verlag, New York, 1992 | MR | Zbl

[3] A. N. Chichkakova, V. V. Chueshev, “Meromorfnye differentsialy i funktsii na konechnoi rimanovoi poverkhnosti”, Mezhdunarodnaya konferentsiya “Differentsialnye uravneniya, teoriya funktsii i prilozheniya”, NGU, Novosibirsk, 2007, 11

[4] O. Forster, Rimanovy poverkhnosti, Mir, M., 1980 | MR

[5] B. A. Dubrovin, Rimanovy poverkhnosti i nelineinye uravneniya, RKhD, M., Izhevsk, 2001