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arXiv · 1810.12787

Root number in integer parameter families of elliptic curves

Julie Desjardins
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Abstract

In a previous article, the author proves that the value of the root number varies in a non-isotrivial family of elliptic curves indexed by one parameter $t$ running through $\mathbb{Q}$. However, a well-known example of Washington has root number $-1$ for every fiber when $t$ runs through $\mathbb{Z}$. Such examples are rare since, as proven in this paper, the root number of the integer fibers varies for a large class of families of elliptic curves. Our results depends on the squarefree conjecture and Chowla's conjecture, and are unconditional in many cases.

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Julie Desjardins. 2018-10-30. Root number in integer parameter families of elliptic curves. https://arxiv.org/abs/1810.12787

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