Periods and Quasiperiods

M. Ram Murty and Purusottam Rath
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M. Ram Murty: Queen’s University, Department of Mathematics and Statistics
Purusottam Rath: Chennai Mathematical Institute

Chapter Chapter 12 in Transcendental Numbers, 2014, pp 55-58 from Springer

Abstract: Abstract In the previous chapter, we proved that the fundamental periods ω 1, ω 2 of a Weierstrass ℘ $$\wp $$ -function whose corresponding g 2, g 3 are algebraic are necessarily transcendental. A similar question arises for the nature of the associated quasi-periods η 1, η 2. We shall show that these are also transcendental whenever g 2 and g 3 are algebraic. To this end, we shall need the following lemmas. Let ℍ $$\mathbb{H}$$ denote the upper half-plane, i.e. the set of complex numbers z with ℑ(z) > 0.

Keywords: Quasiperiods; Fundamental Period; Complex Numbers; Previous Chapter; Weierstrass (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-1-4939-0832-5_12

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