标题： Chebotarev定理的实数域和有限域版本 显示英文标题

标题： Real and finite field versions of Chebotarev's theorem

摘要： 切巴塔廖夫关于单位根的定理指出，所有素数阶傅里叶矩阵的极小式都不为零。 这个结果已经被多次重新发现，并通过不同的技术进行了证明。 我们遵循埃文斯和伊萨克斯的证明，并将原始结果推广到实数版本和有限域上的版本。 对于后者，我们能够移除有限域特征与矩阵大小之间的条件，并且通过张大大降低了特征的一个充分下界。 直接应用包括一个特定的实数相位检索问题以及最近关于指数的里斯基的一结果。 显示英文摘要

摘要： Chebotarev's theorem on roots of unity states that all minors of the Fourier matrix of prime size are non-vanishing. This result has been rediscovered several times and proved via different techniques. We follow the proof of Evans and Isaacs and generalize the original result to a real version and a version over finite fields. For the latter, we are able to remove an order condition between the characteristic of the field and the size of the matrix as well as decrease a sufficient lower bound on the characteristic by Zhang considerably. Direct applications include a specific real phase retrieval problem as well as a recent result for Riesz bases of exponentials.