The Deficiency of being a Congruence Group for Veech Groups of Origamis

Abstract Entire modular forms of weights and for the congruence group Γ0(4N) are constructed, which will be useful for revealing the arithmetical sense of additional terms in formulas for the number of representations of positive integers by quadratic forms in 7 and 9 variables.

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Power moments of Hecke eigenvalues for congruence group

Journal of Number Theory ◽

10.1016/j.jnt.2018.10.006 ◽

2019 ◽

Vol 198 ◽

pp. 139-158 ◽

Cited By ~ 1

Author(s):

Ping Song ◽

Wenguang Zhai ◽

Deyu Zhang

Keyword(s):

Congruence Group ◽

Hecke Eigenvalues ◽

Power Moments

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Scissors congruence group and homology

Scissors Congruences, Group Homology and Characteristic Classes - Nankai Tracts in Mathematics ◽

10.1142/9789812810335_0002 ◽

2001 ◽

pp. 9-15

Keyword(s):

Congruence Group ◽

Scissors Congruence

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Congruence Veech groups

Israel Journal of Mathematics ◽

10.1007/s11856-016-1366-x ◽

2016 ◽

Vol 214 (2) ◽

pp. 885-930

Author(s):

Myriam Finster

Keyword(s):

Veech Groups

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Fundamental domains and generators for lattice Veech groups

Commentarii Mathematici Helvetici ◽

10.4171/cmh/406 ◽

2017 ◽

Vol 92 (1) ◽

pp. 57-83 ◽

Cited By ~ 2

Author(s):

Ronen Mukamel

Keyword(s):

Fundamental Domains ◽

Veech Groups

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Veech groups without parabolic elements

Duke Mathematical Journal ◽

10.1215/s0012-7094-06-13326-4 ◽

2006 ◽

Vol 133 (2) ◽

pp. 335-346 ◽

Cited By ~ 13

Author(s):

Pascal Hubert ◽

Erwan Lanneau

Keyword(s):

Veech Groups

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The automorphism groups of the congruence group and of some of its subgroups in finite Euclidean planes

Journal of Geometry ◽

10.1007/bf01225288 ◽

1984 ◽

Vol 23 (1) ◽

pp. 83-93 ◽

Cited By ~ 1

Author(s):

Helmut Siemon

Keyword(s):

Automorphism Groups ◽

Congruence Group ◽

Euclidean Planes

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A Normal form for a Matrix under the Unitary Congruence Group

Canadian Journal of Mathematics ◽

10.4153/cjm-1961-059-8 ◽

1961 ◽

Vol 13 ◽

pp. 694-704 ◽

Cited By ~ 44

Author(s):

D. C. Youla

Keyword(s):

Normal Form ◽

Unitary Matrix ◽

Alternative Derivation ◽

Congruence Group ◽

Square Roots ◽

Number Of Zeros ◽

Unitary Congruence ◽

Image Position ◽

Square Matrix

Let C be a square matrix with complex elements. If C = C' (C' denotes the transpose of C) there exists a unitary matrix U such that(1)where the μ's are the non-negative square roots of the eigenvalues μ12, μ22, … , μn2 of C*C (C* is the adjoint of C) (2). If C is skew-symmetric, that is, C= — C”, there exists a unitary matrix U such that(2)where(3)and the α's are the positive square roots of the non-zero eigenvalues α12, α22, … , αk2 of C*C (1). Clearly rank C = 2k and the number of zeros appearing in (2) is n — 2k. Both (1) and (2) are classical. In a recent paper (3) Stander and Wiegman, apparently unaware of (1), give an alternative derivation of (2) with its appropriate generalization to quaternions.

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