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VII.—On Eisenstein's Continued Fractions

Published online by Cambridge University Press:  14 March 2016

Thomas Muir
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Extract

In Crelle's Journal for 1844, at the end of a paper on Cubic Forms, Eisenstein gives the following results:—

where m is any odd number and ρ a primitive root of the equation zm = 1;

where

No demonstrations are given of these identities; but they are said by the author to be only particular cases of a very general equation, the complete theory connected with which he hoped to give on another occasion.

At p. 193 of the same volume of Crelle he returns to the subject, not however for the purpose of giving the promised theory, but to add several other results similar to those before given.

Type
Research Article
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 28 , Issue 1 , 1877 , pp. 135 - 143
Copyright
Copyright © Royal Society of Edinburgh 1876

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References

page 135 note * Crelle xxvii. pp. 78, 79.

page 142 note * Trans. R.S.E. 1875–6.