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Expansion of the Inhomogeneous Modular Transformations with Modular Group Properties

Year 2021, Volume: 14 Issue: 2, 453 - 463, 31.08.2021
https://doi.org/10.18185/erzifbed.936882

Abstract

In this study, inhomogeneous modular groups and their basic properties are examined, and the relationships between homogeneous and inhomogeneous linear transformation concepts are discussed. The definition of the modular group is demonstrated by using inhomogeneous linear transformations. With the help of modular group conditions, the upper half-plane is defined with the help of the images under the elements of the modular group gama and the formation of inhomogeneous modular transformations on different transformations is examined. In addition, the theorem about the cases of the modular group has been determined with a distinct method

References

  • Apostol, T. M. (1976). “Modular functions and Dirichlet series in number theory”, Graduate texts in mathematics, Springer-Verleng, New York.
  • Wilson, L. G. 1987. “A Family of Modular Functions Arising from the Theta Function”, Proc, London math. Soc. (3), 55.
  • Lehner, J. (1965). “A short course in automorphic functions”, University of Maryland.
  • Swinnerton-Dyer, H.P.F. and Birch B. J. (1975). “Modular functions of one variable IV”, Lecture notes in Math., Springer Verlag, Berlin-Heidelberg New York, 476, 2-32.

Modüler Grup Özellikleri İle İnhomojen Modüler Grupların Genişlemesi

Year 2021, Volume: 14 Issue: 2, 453 - 463, 31.08.2021
https://doi.org/10.18185/erzifbed.936882

Abstract

Bu çalışmada inhomojen modüler gruplar ve onların temel özellikleri incelenerek homojen, inhomojen lineer dönüşüm kavramları arasındaki ilişkiler ele alınmıştır. Inhomojen lineer dönüşümler kullanılarak modüler grubun tanımı gösterilmiştir. Modüler grup koşulları yardımı ile Γmodüler grubunun elemanları altındaki görüntüleri yardımıyla üst yarı düzlem tanımlanıp inhomojen modüler dönüşümlerin farklı dönüşümler üzerine oluşturulması incelenmiştir. Ayrıca, modüler grubun durumları ile ilgili teorem değişik bir yöntemle kanıtlanmıştır.

References

  • Apostol, T. M. (1976). “Modular functions and Dirichlet series in number theory”, Graduate texts in mathematics, Springer-Verleng, New York.
  • Wilson, L. G. 1987. “A Family of Modular Functions Arising from the Theta Function”, Proc, London math. Soc. (3), 55.
  • Lehner, J. (1965). “A short course in automorphic functions”, University of Maryland.
  • Swinnerton-Dyer, H.P.F. and Birch B. J. (1975). “Modular functions of one variable IV”, Lecture notes in Math., Springer Verlag, Berlin-Heidelberg New York, 476, 2-32.
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Details

Primary Language English
Subjects Engineering
Journal Section Makaleler
Authors

İsmet Yıldız 0000-0001-7544-4835

Kezban Altun 0000-0002-5132-2355

Betül Öztürk 0000-0002-3109-3479

Hasan Şahin 0000-0002-5227-5300

Publication Date August 31, 2021
Published in Issue Year 2021 Volume: 14 Issue: 2

Cite

APA Yıldız, İ., Altun, K., Öztürk, B., Şahin, H. (2021). Expansion of the Inhomogeneous Modular Transformations with Modular Group Properties. Erzincan University Journal of Science and Technology, 14(2), 453-463. https://doi.org/10.18185/erzifbed.936882