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On Grimm's conjecture in algebraic number fields

✍ Scribed by Neela S Sukthankar (Rege)

Publisher
Elsevier Science
Year
1973
Weight
511 KB
Volume
76
Category
Article
ISSN
1385-7258

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πŸ“œ SIMILAR VOLUMES

On Grimm's conjecture in algebraic numbe
On Grimm's conjecture in algebraic number fields. II
✍ Neela S Sukthankar (Rege) πŸ“‚ Article πŸ“… 1975 πŸ› Elsevier Science βš– 513 KB

Let k be an algebraic number field of degree n over &, n =rl+ 2rs and let WI, . . . . Wn be a fixed basis of the ring of integers o over 2. For z E k, z= zB1 qwt, at E (1, c(z, R) will denote the disc {c E k, c= 2 biwi, bt E Q, ~i1~-bt12=zfi} and ~(0, R) will be the disc (CE k, 5= zbtiwr, xb; (log ]

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Let 2 be the ring of rational integers. For n E Z, w(n) denotes the number of distinct prime factors of n. In [4] Ramachandra, Shorey and Tijdeman proved that if 1 k, where c > 0 is an effectively computable constant. In this paper, we will generalise this problem to the case of imaginary quadratic

Leopoldt's conjecture for imaginary Galo
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✍ Norbert Klingen πŸ“‚ Article πŸ“… 1990 πŸ› Elsevier Science 🌐 English βš– 744 KB

In studying Leopoldt's conjecture for Galois number fields a sufficient condition is proposed which includes the known criteria and moreover refers only to the character table of the Galois group in question. Hence it may easily be checked. Tables of the computations are given. New examples, if only