The Upper Half-Plane

Murty, M. Ram; Dewar, Michael; Graves, Hester

doi:10.1007/978-981-10-2651-5_13

M. Ram Murty⁴,
Michael Dewar⁵ &
Hester Graves⁶

Part of the book series: HBA Lecture Notes in Mathematics ((IMSLNM))

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Abstract

Show that

$$ \left( {\begin{array}{*{20}c} a & b \\ c & d \\ \end{array} } \right)z = \frac{az + b}{cz + d} $$

defines as action of $ {\text{GL}}_{2}^{ + } ({\mathbb{R}}) $ on $ {\mathbb{H}} $.

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Authors and Affiliations

Department of Mathematics and Statistics, Queen’s University, Kingston, ON, Canada
M. Ram Murty
Queen’s University, Kingston, ON, Canada
Michael Dewar
University of Michigan, Ann Arbor, MI, USA
Hester Graves

Authors

M. Ram Murty
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Michael Dewar
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Hester Graves
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Correspondence to M. Ram Murty .

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Murty, M.R., Dewar, M., Graves, H. (2016). The Upper Half-Plane. In: Problems in the Theory of Modular Forms. HBA Lecture Notes in Mathematics(). Springer, Singapore. https://doi.org/10.1007/978-981-10-2651-5_13

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DOI: https://doi.org/10.1007/978-981-10-2651-5_13
Published: 26 November 2016
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-2651-5
Online ISBN: 978-981-10-2651-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)

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