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Note on a polynomial of Emma Lehmer. (English) Zbl 0732.11056
This is more than “a note on a polynomial of Emma Lehmer”. The author obtains important results on the units of a certain parametric family of real quintic fields previously considered by E. Lehmer and later by R. Schoof and L. Washington. In fact the results were also independently obtained by O. Lecacheux [Ann. Inst. Fourier 40, No.2, 237-253 (1990)]. Using the modular curve \(X_ 1(25)\) as a covering of \(X_ 0(25)\), the author obtains E. Lehmer’s units as modular units, and finds expressions for certain Gauss sums as values of modular units on \(X_ 1(25)\). It is a very interesting area of research to study units of certain cyclic extensions of \({\mathbb{Q}}\) arising from the modular covering \(X_ 1(N)\to X_ 0(N)\).

MSC:
11R20 Other abelian and metabelian extensions
11R27 Units and factorization
11G16 Elliptic and modular units
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