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Research output: Working paper

**Congruence properties of induced representations.** / Mayer, Dieter; Momeni, Arash; Venkov, Alexei.

Research output: Working paper

Mayer, D, Momeni, A & Venkov, A 2012 'Congruence properties of induced representations' arXiv.org, pp. 1210.5979.

Mayer, D., Momeni, A., & Venkov, A. (2012). *Congruence properties of induced representations*. (pp. 1210.5979). arXiv.org.

Mayer D, Momeni A, Venkov A. 2012. Congruence properties of induced representations. arXiv.org. pp. 1210.5979.

Mayer, Dieter, Arash Momeni, and Alexei Venkov *Congruence properties of induced representations*. 1210.5979. arXiv.org. 2012, 14 p.

Mayer D, Momeni A, Venkov A. Congruence properties of induced representations. arXiv.org. 2012, p. 1210.5979.

Mayer, Dieter ; Momeni, Arash ; Venkov, Alexei. / **Congruence properties of induced representations**. arXiv.org, 2012. pp. 1210.5979

@techreport{b63cf58b4ddb451ebbf337de42292203,

title = "Congruence properties of induced representations",

abstract = "In this paper we study representations of the projective modular group induced from the Hecke congruence group of level 4 with Selberg\{textquoteleft}s character. We show that the well known congruence properties of Selberg\{textquoteleft}s character are equivalent to the congruence properties of the induced representations. Concerning this congruence property, it turns out that working with the induced representations is easier than with Selberg\{textquoteleft}s character itself. We also show that the kernels of the induced representations determine an infinite sequence of noncongruence groups, whose noncongruence property can not be detected by Zograf\{textquoteleft}s geometric method. They belong to the class of character groups of type $\rm I$ for the principal congruence subgroup $\Gamma(4)$ and have, contrary to the noncongruence groups determined by Selberg\{textquoteleft}s character which all have genus $g=0$, arbitrary genus $g\geq 0$.",

keywords = "Number Theory (math.NT), 11F70 (Primary) 30F35, 20H05, 20C15, 20H10, 20E40 (Secondary)",

author = "Dieter Mayer and Arash Momeni and Alexei Venkov",

year = "2012",

language = "English",

pages = "1210.5979",

publisher = "arXiv.org",

type = "WorkingPaper",

institution = "arXiv.org",

}

TY - UNPB

T1 - Congruence properties of induced representations

AU - Mayer,Dieter

AU - Momeni,Arash

AU - Venkov,Alexei

PY - 2012

Y1 - 2012

N2 - In this paper we study representations of the projective modular group induced from the Hecke congruence group of level 4 with Selberg's character. We show that the well known congruence properties of Selberg's character are equivalent to the congruence properties of the induced representations. Concerning this congruence property, it turns out that working with the induced representations is easier than with Selberg's character itself. We also show that the kernels of the induced representations determine an infinite sequence of noncongruence groups, whose noncongruence property can not be detected by Zograf's geometric method. They belong to the class of character groups of type $\rm I$ for the principal congruence subgroup $\Gamma(4)$ and have, contrary to the noncongruence groups determined by Selberg's character which all have genus $g=0$, arbitrary genus $g\geq 0$.

AB - In this paper we study representations of the projective modular group induced from the Hecke congruence group of level 4 with Selberg's character. We show that the well known congruence properties of Selberg's character are equivalent to the congruence properties of the induced representations. Concerning this congruence property, it turns out that working with the induced representations is easier than with Selberg's character itself. We also show that the kernels of the induced representations determine an infinite sequence of noncongruence groups, whose noncongruence property can not be detected by Zograf's geometric method. They belong to the class of character groups of type $\rm I$ for the principal congruence subgroup $\Gamma(4)$ and have, contrary to the noncongruence groups determined by Selberg's character which all have genus $g=0$, arbitrary genus $g\geq 0$.

KW - Number Theory (math.NT)

KW - 11F70 (Primary) 30F35, 20H05, 20C15, 20H10, 20E40 (Secondary)

M3 - Working paper

SP - 1210.5979

BT - Congruence properties of induced representations

PB - arXiv.org

ER -