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On the periods of the exponential and elliptic functions

Published online by Cambridge University Press:  24 October 2008

D. W. Masser
D. W. Masser
Affiliation:
Trinity College, Cambridge
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Extract

Let ℘ be a Weierstrass elliptic function satisfying the differential equation

and let ζ(z) be the associated Weierstrass ζ-function satisfying (z) = −℘(z). Corresponding to a pair of fundamental periods ω1, ω2 of ℘(z), there is a pair of quasi-periods η1, η2 of ζ(z) defined by

and we have ηi = 2ζ(ωi/2) for i = 1, 2.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 73 , Issue 2 , March 1973 , pp. 339 - 350
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

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