标题： 有限域中间扩张中具有指定迹的正规和原始正规元素 显示英文标题

标题： Normal and primitive normal elements with prescribed traces in intermediate extensions of finite fields

摘要： 在本文中，我们研究有限域扩张中具有在若干中间扩张中指定迹的元素的存在性和分布情况，这些中间扩张也可能是正规的或原根的。 在前一种情况下，我们完全描述了此类元素存在的条件，并提供了这些元素的显式计数。 在后一种情况下，我们提供了渐近结果。 显示英文摘要

摘要： In this article, we study the existence and distribution of elements in finite field extensions with prescribed traces in several intermediate extensions that are also either normal or primitive normal. In the former case, we fully characterize the conditions under which such elements exist and provide an explicit enumeration of these elements. In the latter case we provide asymptotic results.