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On Grimm's conjecture in algebraic number fields. II

✍ Scribed by Neela S Sukthankar (Rege)

Publisher
Elsevier Science
Year
1975
Weight
513 KB
Volume
78
Category
Article
ISSN
1385-7258

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✦ Synopsis

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 ]z])lln (log log Ix])'" (log log log jzj)-in. Recently it is proved by RAMACHANDRA, SHOREY and TIJDEMAN [l], that in the case of rational integers g > (log n)3

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On Grimm's conjecture in algebraic numbe
On Grimm's conjecture in algebraic number fields-III
✍ Neela S Sukthankar (REGE) πŸ“‚ Article πŸ“… 1977 πŸ› Elsevier Science βš– 299 KB

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