Abstract

Primitive Representations and the Modular Group

Highlights

  • We find some elements of modular group PSL(2,Z) that moves α to α−, α to −α− and α to −α

  • Binary quadratic form is one of the subjects treated in elementary number theory

  • Another subject treated in elementary number theory is the possibility of representing a positive integer as a sum of two squares and difference of two squares

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Summary

Introduction

Binary quadratic form is one of the subjects treated in elementary number theory. Another subject treated in elementary number theory is the possibility of representing a positive integer as a sum of two squares and difference of two squares. We find some elements of modular group PSL(2,Z) that moves α to α− , α to −α− and α to −α. We determine the elements of G and conditions on a, b, c when αG We describe the elements of G that moves real quadratic irrational numbers to their conjugates.

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