Geodesic
Multiplicative Functions with Matrix Characters on Compact Riemann Surfaces
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 1, pp. 31-40 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The theory of multiplicative functions and Prym differentials for special (scalar) characters on compact Riemann surfaces has many applications in the theory of functions, in analytic numbers theory and in mathematical physics. In this article we proove existence of matrix multiplicative functions and Prym $m$-differentials for every matrix characters with values in $GL(n;\mathbb C)$ on compact Riemann surfaces.
Keywords: compact Riemann surface, multiplicative functions and Prym differentials, matrix characters, Fuchsian group.
Mots-clés : theta Poincaré series 
@article{JSFU_2009_2_1_a2,
     author = {Alena A. Bespomestnych and Victor V. Chueshev},
     title = {Multiplicative {Functions} with {Matrix} {Characters} on {Compact} {Riemann} {Surfaces}},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {31--40},
     year = {2009},
     volume = {2},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2009_2_1_a2/}
}
TY  - JOUR
AU  - Alena A. Bespomestnych
AU  - Victor V. Chueshev
TI  - Multiplicative Functions with Matrix Characters on Compact Riemann Surfaces
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2009
SP  - 31
EP  - 40
VL  - 2
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JSFU_2009_2_1_a2/
LA  - ru
ID  - JSFU_2009_2_1_a2
ER  - 
%0 Journal Article
%A Alena A. Bespomestnych
%A Victor V. Chueshev
%T Multiplicative Functions with Matrix Characters on Compact Riemann Surfaces
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2009
%P 31-40
%V 2
%N 1
%U http://geodesic.mathdoc.fr/item/JSFU_2009_2_1_a2/
%G ru
%F JSFU_2009_2_1_a2
Alena A. Bespomestnych; Victor V. Chueshev. Multiplicative Functions with Matrix Characters on Compact Riemann Surfaces. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 1, pp. 31-40. http://geodesic.mathdoc.fr/item/JSFU_2009_2_1_a2/

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

[2] P. Appell, “Generalisation des fonctions doublement periodiques de seconde espece”, J. Math. Pures Appl. Ser. 3, 9 (1883), 5–24

[3] O. Haupt, “Zur theorie der Prymschen Funktionen 1 und $N$ Ordnung”, Math. Ann., 77 (1915), 24–64 | DOI | MR | Zbl

[4] K. Iwasawa, Algebraic functions, Trans. Math. Monographs., 188, Providence, RI, 1993 | MR

[5] H. M. Farkas, I. Kra, Riemann surfaces, Graduate Texts in Math., 71, Springer-Verlag, 1992 | MR | Zbl

[6] V. V. Chueshev, Geometricheskaya teoriya funktsii na kompaktnoi rimanovoi poverkhnosti, KemGU, Kemerovo, 2005 | Zbl

[7] S. L. Krushkal, Kvazikonformnye otobrazheniya i rimanovy poverkhnosti, Nauka, Novosibirsk, 1975 | MR | Zbl

[8] Dzh. Springer, Vvedenie v teoriyu rimanovykh poverkhnostei, IL, M., 1960