Gotthold Eisenstein worked on a variety of topics including quadratic and cubic forms, the reciprocity theorem for cubic residues, quadratic partition of prime numbers and reciprocity laws. He was born in Berlin on 16 April 1823, suffered bad health throughout his life, and died in Berlin on 11 October 1852, aged twenty-nine. The numbers of the form a plus b omega, where omega is a complex cube root of unity, are named for him as the Eisenstein integers, and so is the Eisenstein criterion on irreducible polynomials.
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Gotthold Eisenstein
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Source Eisenstein integer (Wikipedia)
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Source Gotthold Eisenstein, Biography (MacTutor History of Mathematics)
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Source Eisenstein Integers (Wikipedia)
Source Eisenstein's criterion - Wikipedia
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Source Eisenstein's criterion - Wikipedia
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Source Gotthold Eisenstein, Biography (MacTutor History of Mathematics)Quick InfoQuote, Quick Info
Born 16 April 1823 Berlin, Germany
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1. Gotthold Eisenstein, Biography (MacTutor History of Mathematics)
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16 April 1823
Summary
Gotthold Eisenstein worked on a variety of topics including quadratic and cubic forms, the reciprocity theorem for cubic residues, quadratic partition of prime numbers and reciprocity laws.
View the SourceEisenstein integer (Wikipedia)
Attributed Works: Eisenstein Integers, Lead sectionQuote, Attributed Works: Eisenstein Integers, Lead section
In mathematics, the Eisenstein integers (named after Gotthold Eisenstein), occasionally also known as Eulerian integers (after Leonhard Euler), are the complex numbers of the form
Eisenstein's criterion - Wikipedia
Principal Result: Eisenstein's Criterion, Lead sentence of the article on the result
This criterion is named after Gotthold Eisenstein.
Proofs Credited: Eisenstein's Criterion, Lead
This criterion is named after Gotthold Eisenstein.
View the SourceEisenstein Integers (Wikipedia)
Principal Result: Eisenstein Integers, Lead sentence of the article on the resultQuote, Principal Result: Eisenstein Integers, Lead sentence of the article on the result
In mathematics, the Eisenstein integers (named after Gotthold Eisenstein), occasionally also known as Eulerian integers (after Leonhard Euler), are the complex numbers of the form z = a + b ω , {\displaystyle z=a+b\omega ,} where a and b are integers and ω = − 1 + i 3 2 = e i 2 π / 3 {\displaystyle \omega ={\frac {-1+i{\sqrt {3}}}{2}}=e^{i2\pi /3}} is a primitive (hence non-real) cube root of unity.
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