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Solvability of systems of diagonal equations over p‐adic local fields
Proceedings of the London Mathematical Society ( IF 1.5 ) Pub Date : 2020-05-04 , DOI: 10.1112/plms.12318
Christopher Skinner 1
Affiliation  

We prove that a system of R diagonal equations of degree d over a finite extension K of Q p has a non‐trivial solution in K if the number of variables exceeds 3 R 2 d 2 (if p > 2 ) or 8 R 2 d 2 (if p = 2 ). As a consequence, a system of R homogeneous equations of degree d over K has a non‐trivial solution in K if the number of variables exceeds ( 8 R 2 d 2 ) 2 d 1 .

中文翻译:

p-adic局部场上对角方程组的可解性

我们证明了 [R 度对角线方程 d 在有限扩展上 ķ p 有一个不平凡的解决方案 ķ 如果变量数量超过 3 [R 2 d 2 (如果 p > 2 ) 要么 8 [R 2 d 2 (如果 p = 2 )。结果, [R 齐次度方程 d 过度 ķ 有一个不平凡的解决方案 ķ 如果变量数量超过 8 [R 2 d 2 2 d - 1个
更新日期:2020-05-04
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