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摘要翻译：
我们用36个偶数θ零的乘积给出了一个判别亏格三雅可比及其[-1]扭的判据。我们还用亏格三曲线的判别式来表示36个θ零的乘积。这些结果本质上是算术性质的，因此增加了以前关于偶数θ零值乘积的C的工作。他们推广了Ritzenthaler和Lachaud关于（2,2,2）等同于椭圆曲线乘积的阿贝尔三元的先前工作。这是2003年Jean-Pierre Serre给Jaap Top的一封信的答复。
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英文标题：
《Twists of genus three Jacobians》
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作者：
Stephen Meagher
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最新提交年份：
2015
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Number Theory 数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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英文摘要：
We give a criterion to distinguish between a genus three Jacobian and its [-1] twist in terms of the product of the 36 even theta nulls. We also express the product of the 36 theta nulls in terms of the discriminant of a genus three curve. The results are arithmetic in nature and thus add to previous work over C on the product of the even theta nulls. They generalize previous work of Ritzenthaler and Lachaud for Abelian threefolds which are (2,2,2) isogenous to a product of elliptic curves. This answers a 2003 of letter of Jean-Pierre Serre to Jaap Top.
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PDF链接：
https://arxiv.org/pdf/0711.0415
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