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These cookies do not store any personal information. The Disquisitiones covers both elementary number theory and parts of the area of mathematics now called algebraic number theory. While recognising the primary importance of logical proof, Gauss also illustrates many theorems with numerical examples.
However, Gauss did not explicitly recognize the concept of a groupwhich is central to modern algebraso he did not use this term. The treatise paved the way for the theory of function fields over a finite field of constants. In section VII, articleGauss proved what can be interpreted as the first non-trivial case of the Riemann hypothesis for curves over finite fields the Hasse—Weil theorem. They must have appeared particularly cryptic to his contemporaries; they can now be read as containing the germs of the theories of L-functions and complex multiplicationin particular.
The Disquisitiones was one of the last mathematical works to be written in scholarly Latin an English translation was not published until In this book Gauss brought together and reconciled results in number theory obtained by mathematicians such as FermatEulerLagrangeand Legendre and added many profound and original results of his own.
Section IV itself develops a proof of quadratic reciprocity ; Section V, which takes up over half of the book, is a comprehensive analysis of binary and ternary quadratic forms. In other projects Wikimedia Commons. By using this site, you agree to aritgmeticae Terms of Use and Privacy Policy. From Wikipedia, the free encyclopedia. From Section IV onwards, much of the work is original. The logical structure of the Disquisitiones theorem statement followed by prooffollowed by corollaries set a standard for later gaus.
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Authors view affiliations Carl Friedrich Gauss. Disquisitiones was the starting point for the work of other 19th century European mathematics and continued to influence 20th century mathematics Illustrates many theorems with numerical examples One of the last mathematical works to be written in scholarly Latin.
Congruent Numbers in General. Pages Congruences of The First Degree. Residues of Powers.
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