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About the Cover: Meromorphic Functions with Doubly Periodic Phase

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Abstract

The phase plot of the function depicted on the cover of this volume is doubly periodic. In this expository paper, we discuss a canonical representation of all functions with doubly periodic phase (argument) in terms of the Weierstrass \(\sigma \)-function. In particular, we point out that the zeros and poles of such a function in a fundamental domain can be prescribed arbitrarily, with the only restriction that their total numbers (counting multiplicities) must coincide.

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Acknowledgements

We thank the referee for pointing out the relation of this topic to elliptic functions of the second kind and for recommending some related references.

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Authors and Affiliations

  1. Institute of Applied Analysis, TU Bergakademie Freiberg, 09596, Freiberg, Germany

    Gunter Semmler & Elias Wegert

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  1. Gunter Semmler
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  2. Elias Wegert
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Correspondence to Elias Wegert.

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Communicated by Mario Bonk.

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Semmler, G., Wegert, E. About the Cover: Meromorphic Functions with Doubly Periodic Phase. Comput. Methods Funct. Theory 18, 1–7 (2018). https://doi.org/10.1007/s40315-018-0236-4

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