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Unimodular integral circulants

Taussky, Olga (1955) Unimodular integral circulants. Mathematische Zeitschrift, 63 (1). pp. 286-289. ISSN 0025-5874. https://resolver.caltech.edu/CaltechAUTHORS:20201022-100905336

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Abstract

Some properties of the "discriminant matrix" (α_i^(S_k))) of a normal algebraic number field of degree n were investigated in two previous notes (1 ,2). Here the α_i form an integral basis of the field and the S_k are the elements of the GALOIS group). In the special case when the α_i form a normal basis various problems concerning group matrices arise, among others, questions concerning unimodular group matrices whose elements are rational integers. If the field is cyclic circulant, matrices appear, i.e. matrices C = (c_(ik)) with c_(ik) = c_(k-i+1) where the suffixes are considered mod n. In particular the following theorem was obtained which will be studied further in the present note.


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https://doi.org/10.1007/bf01187938DOIArticle
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Additional Information:© 1955 Springer. (Eingegangen am 7, März 1955) In memoriam ISSAI SCHUR. This work was supported (in part) by the Office of Naval Research.
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Office of Naval Research (ONR)UNSPECIFIED
Issue or Number:1
Record Number:CaltechAUTHORS:20201022-100905336
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20201022-100905336
Official Citation:Taussky, O. Unimodular integral circulants. Math Z 63, 286–289 (1955). https://doi.org/10.1007/BF01187938
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106215
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:22 Oct 2020 22:54
Last Modified:22 Oct 2020 22:54

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