Numerical verification of the Birch and Swinnerton-Dyer conjecture for hyperelliptic curves of higher genus over $\mathbb Q$ up to squares

@article{Bommel2017NumericalVO,
  title={Numerical verification of the Birch and Swinnerton-Dyer conjecture for hyperelliptic curves of higher genus over \$\mathbb Q\$ up to squares},
  author={R. V. Bommel},
  journal={arXiv: Number Theory},
  year={2017}
}
  • R. V. Bommel
  • Published 2017
  • Mathematics
  • arXiv: Number Theory
  • The Birch and Swinnerton-Dyer conjecture has been numerically verified for the Jacobians of 32 modular hyperelliptic curves of genus 2 by Flynn, Lepr\'evost, Schaefer, Stein, Stoll and Wetherell, using modular methods. In the calculation of the real period, there is a slight inaccuracy, which might give problems for curves with non-reduced components in the special fibre of their N\'eron model. In this present paper we explain how the real period can be computed, and how the verification has… CONTINUE READING
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