Geodesic
Interaction of Hecke–Shimura rings acting on theta-series
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 28, Tome 418 (2013), pp. 8-27 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The paper considers principal features of interactions (transfer homomorphisms) for Hecke–Shimura rings of integral symplectic groups and integral orthogonal groups of positive definite integral quadratic forms both operating on theta-series of positive definite quadratic forms by Hecke operators. 
@article{ZNSL_2013_418_a1,
     author = {A. Andrianov},
     title = {Interaction of {Hecke{\textendash}Shimura} rings acting on theta-series},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {8--27},
     year = {2013},
     volume = {418},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_418_a1/}
}
TY  - JOUR
AU  - A. Andrianov
TI  - Interaction of Hecke–Shimura rings acting on theta-series
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2013
SP  - 8
EP  - 27
VL  - 418
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2013_418_a1/
LA  - en
ID  - ZNSL_2013_418_a1
ER  - 
%0 Journal Article
%A A. Andrianov
%T Interaction of Hecke–Shimura rings acting on theta-series
%J Zapiski Nauchnykh Seminarov POMI
%D 2013
%P 8-27
%V 418
%U http://geodesic.mathdoc.fr/item/ZNSL_2013_418_a1/
%G en
%F ZNSL_2013_418_a1
A. Andrianov. Interaction of Hecke–Shimura rings acting on theta-series. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 28, Tome 418 (2013), pp. 8-27. http://geodesic.mathdoc.fr/item/ZNSL_2013_418_a1/

[1] Mat. Sb. (N.S.), 131(173):3 (1986), 275–292 | MR | Zbl

[2] A. N. Andrianov, Quadratic Forms and Hecke Operators, Grundlehren math. Wiss., 286, Springer-Verlag, Berlin–Heidelberg, 1987 | DOI | MR | Zbl

[3] A. N. Andrianov, “Simmetrii garmonicheskikh teta-funktsii tselochislennykh kvadratichnykh form”, Uspekhi mat. nauk, 50:4 (1995), 3–44 | MR | Zbl

[4] A. N. Andrianov, “Garmonicheskie teta-ryady i operatory Gekke”, Algebra i analiz, 8:5 (1996), 1–31 | MR | Zbl

[5] A. N. Andrianov, “Vokrug pod'ema Ikedy”, Funkts. analiz i ego prilozh., 35:2 (2001), 70–74 | DOI | MR | Zbl

[6] A. N. Andrianov, “Vzeta-funktsii ortogonalnykh grupp odnoklassnykh polozhitelno opredelennykh kvadratichnykh form”, Uspekhi mat. nauk, 61:6 (2006), 3–44 | DOI | MR | Zbl

[7] A. Andrianov, “Interaction sums and action of Hecke operators on theta-series”, Acta Arith., 140 (2009), 271–304 | DOI | MR | Zbl

[8] A. Andrianov, “On interaction of Hecke–Shimura rings: symplectic versus orthogonal”, Acta Arith., 151:1 (2012), 97–107 | DOI | MR