ON SUBORBITAL GRAPH FOR THE CONGRUENCE SUBGROUP

2020 ◽  
Vol 125 (2) ◽  
pp. 163-175
Author(s):  
Zeynep Şanlı ◽  
Mehmet Akbaş
Keyword(s):  
Congruence Subgroup ◽  
Suborbital Graph

scholarly journals The profinite completion of multi-EGS groups

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Anitha Thillaisundaram ◽  
Jone Uria-Albizuri
Keyword(s):  
Congruence Subgroup ◽  
Profinite Completion ◽  
Congruence Subgroup Property

AbstractThe class of multi-EGS groups is a generalisation of the well-known Grigorchuk–Gupta–Sidki (GGS-)groups. Here we classify branch multi-EGS groups with the congruence subgroup property and determine the profinite completion of all branch multi-EGS groups. Additionally, our results show that branch multi-EGS groups are just infinite.

scholarly journals On Elliptic Curves with Complex Multiplication as Factors of the Jacobians of Modular Function Fields

1971 ◽  
Vol 43 ◽  
pp. 199-208 ◽  
Author(s):  
Goro Shimura
Keyword(s):  
Elliptic Curves ◽  
Cusp Form ◽  
Mellin Transform ◽  
Quadratic Field ◽  
Congruence Subgroup ◽  
Function Fields ◽  
Complex Multiplication ◽  
Modular Function ◽  
Imaginary Quadratic Field

1. As Hecke showed, every L-function of an imaginary quadratic field K with a Grössen-character γ is the Mellin transform of a cusp form f(z) belonging to a certain congruence subgroup Γ of SL2(Z). We can normalize γ so that

BASES FOR Sk(Γ1(4)) AND FORMULAS FOR EVEN POWERS OF THE JACOBI THETA FUNCTION

2013 ◽  
Vol 09 (08) ◽  
pp. 1973-1993 ◽  
Author(s):  
SHINJI FUKUHARA ◽  
YIFAN YANG
Keyword(s):  
Eisenstein Series ◽  
Theta Function ◽  
Congruence Subgroup ◽  
Negative Integer ◽  
Cusp Forms ◽  
Jacobi Theta Function

We find a basis for the space Sk(Γ1(4)) of cusp forms of weight k for the congruence subgroup Γ1(4) in terms of Eisenstein series. As an application, we obtain formulas for r2k(n), the number of ways to represent a non-negative integer n as sums of 2k integer squares.

scholarly journals Torsion classes in the cohomology of congruence subgroups

1989 ◽  
Vol 105 (2) ◽  
pp. 241-248 ◽  
Author(s):  
Dominique Arlettaz
Keyword(s):  
Prime Number ◽  
Congruence Subgroup ◽  
Surjective Homomorphism ◽  
Congruence Subgroups ◽  
Image Position ◽  
Homology Stability

For any prime number p, let Γn, p denote the congruence subgroup of SLn(ℤ) of level p, i.e. the kernel of the surjective homomorphism fp: SLn(ℤ) → SLn(p) induced by the reduction mod p (Fp is the field with p elements). We defineusing upper left inclusions Γn, p ↪ Γn+1, p. Recall that the groups Γn, p are homology stable with M-coefficients, for instance if M = ℚ, ℤ[1/p], or ℤ/q with q prime and q ╪ p: Hi(Γn, p; M) ≅ Hi(Γp; M) for n ≥ 2i + 5 from [7] (but the homology stability fails if M = ℤ or ℤ/p).

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