Schinzel, Andrzej; Zassenhaus, Hans A refinement of two theorems of Kronecker. (English) Zbl 0128.03402 Mich. Math. J. 12, 81-85 (1965). The authors prove the following two theorems, which are refinements of two results of L. Kronecker [J. Reine Angew. Math. 53, 173–175 (1857; Zbl 02750398)]. Theorem 1. If an algebraic integer \(\alpha\ne 0\) is not a root of unity, and if \(2s\) among its conjugates \(\alpha_i\) \((i = 1, 2, \ldots, n)\) are complex, then \(\displaystyle \max_{1\le i\le n} \vert\alpha_i\vert > 1 + 4^{-s-2}\). Theorem 2. If a totally real algebraic integer \(\beta\) is different from \(2 \cos \rho\pi\) \((\rho\) rational), and \(\{\beta_i\}\) \((i = 1, 2, \ldots, n)\) is the set of its conjugates, then \(\displaystyle\max \{\beta_i\} > 2 + 4^{-2n-3}\). Reviewer: Sunder Lal (Chandigarh) Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 5 ReviewsCited in 32 Documents MSC: 11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure Keywords:algebraic integers; house; maximum modulus of conjugates Citations:Zbl 02750398 × Cite Format Result Cite Review PDF Full Text: DOI