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Published **1955**
in Leiden .

Written in English

- Congruences and residues

**Edition Notes**

Other titles | The characters of binary modulary congruence groups. |

Classifications | |
---|---|

LC Classifications | QA242 .V3 |

The Physical Object | |

Pagination | 54, [1] p. |

Number of Pages | 54 |

ID Numbers | |

Open Library | OL6260376M |

LC Control Number | 58042107 |

OCLC/WorldCa | 23615529 |

Two congruence classes modulo n are either disjoint or identical. Proof. If [a] n and [b] n are disjoint there is nothing to prove. Suppose then that [a] n \[b] n 6= ;. Then there is an integer b such that b 2[a] n and b 2[c] n. So b a (mod n) and b c mod n). By the symmetry and transitivity properties of congruence File Size: KB. 2 The Modular Group and Elliptic Curves3 3 Modular Forms for Congruence Subgroups4 4 Sums of Four Squares5 Abstract First we expand the connection between the modular group and ellip-tic curves by de ning certain subgroups of the modular group, known as \congruence subgroups", and stating their relation to \enhanced elliptic curves". Presented is the idea of the congruence of binary gaskets generated using modular arithmetic operations on a parent array. It is seen that the binary Cited by: 2. The characters of the binary modular congruence group Kutzko, Philip C., Bulletin of the American Mathematical Society, Selberg type zeta function for the Hilbert modular group of a real quadratic field Gon, Yasuro, Proceedings of the Japan Academy, Series A, Mathematical Sciences,

In his Ph.D thesis (See The characters of binary modular congruence group, Bulletin of the American Mathematical Society. 79 (), no. 4 Stack Exchange Network Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and. The concept of Hecke operators was so simple and natural that, soon after Hecke's work, scholars made the attempt to develop a Hecke theory for modular forms, such as Siegel modular forms. As this theory developed, the Hecke operators on spaces of modular forms in several variables were found to have arithmetic meaning. Specifically, the theory provided a framework for discovering certain. Kloosterman solved the general case in two papers The behaviour of general theta functions under the modular group and the characters of binary modular congruence groups which occupy pages of the Annals of Mathematics in Kloosterman was promoted to professor at the University of Leiden in , a post he retained until his death. [B7] The behaviour of general theta functions under the modular group and the characters of binary modular congruence groups I, II. Annals of Math. 47 (), [B8] The characters of binary modulary congruence groups. Proc. Intern. Congress of Mathematicians , C.

The higher commutator is a higher arity generalization of the binary commutator, which was first defined in full generality in the seventies. While the binary commutator has a rich theory for congruence modular varieties, the theory of the higher arity commutator was poorly understood outside of the context of congruence permutability. H. D. Kloosterman, The behaviour of general theta functions under the modular group and the characters of binary modular congruence groups. I, Ann. of . The modular group is a discrete group of transformations of the complex upper half-plane $ H = \{ {z = x + iy }: {y > 0 } \} $(sometimes called the Lobachevskii plane or Poincaré upper half-plane) and has a presentation with generators $ T: z \rightarrow z + 1 $ and $ S: z \rightarrow - 1 / z $, and relations $ S ^ {2} = (ST) ^ {3} = 1. [Klos] H. D. Kloosterman, "The behaviour of general theta functions under the modular group and the characters of binary modular congruence groups. I," Ann. .

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