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arXiv · 2101.06530

Values of zeta functions of arithmetic surfaces at $s=1$

S. Lichtenbaum·N. Ramachandran
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Abstract

We show that the recent conjecture of the first-named author for the special value at $s=1$ of the zeta function of an arithmetic surface is equivalent to the Birch-Swinnerton-Dyer conjecture for the Jacobian of the generic fibre.

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S. Lichtenbaum, N. Ramachandran. 2021-01-16. Values of zeta functions of arithmetic surfaces at $s=1$. https://doi.org/10.1017/s1474748022000093

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