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Efficient Computation of Rankin p-Adic L-Functions

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Computations with Modular Forms

Part of the book series: Contributions in Mathematical and Computational Sciences ((CMCS,volume 6))

Abstract

We present an efficient algorithm for computing certain special values of Rankin triple product p-adic L-functions and give an application of this to the explicit construction of rational points on elliptic curves.

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References

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Acknowledgements

This paper would have been neither started nor finished without the constant help and encouragement of Henri Darmon. It is a pleasure to thank him for this, and to thank also David Loeffler, Victor Rotger and Andrew Wiles for enlightening discussions, and the anonymous referee for many useful comments. This work was supported in part by a grant from the European Research Council (204083).

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Authors and Affiliations

  1. Mathematical Institute, 24-29 St Giles’, Oxford, OX1 3LB, England, UK

    Alan G. B. Lauder

Authors
  1. Alan G. B. Lauder
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Correspondence to Alan G. B. Lauder .

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Editors and Affiliations

  1. Interdisciplinary Center for Scientific Computing, Universität Heidelberg, Heidelberg, Baden-Württemberg, Germany

    Gebhard Böckle

  2. UR Mathématiques, Faculté des Sciences, de la Technologie et de la Communication, Luxembourg, Luxembourg

    Gabor Wiese

Additional information

For Roger Heath-Brown on his sixtieth birthday.

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Lauder, A.G.B. (2014). Efficient Computation of Rankin p-Adic L-Functions. In: Böckle, G., Wiese, G. (eds) Computations with Modular Forms. Contributions in Mathematical and Computational Sciences, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-03847-6_7

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