Lectures on Number TheoryDuring the academic year 1916-1917 I had the good fortune to be a student of the great mathematician and distinguished teacher Adolf Hurwitz, and to attend his lectures on the Theory of Functions at the Polytechnic Institute of Zurich. After his death in 1919 there fell into my hands a set of notes on the Theory of numbers, which he had delivered at the Polytechnic Institute. This set of notes I revised and gave to Mrs. Ferentinou-Nicolacopoulou with a request that she read it and make relevant observations. This she did willingly and effectively. I now take advantage of these few lines to express to her my warmest thanks. Athens, November 1984 N. Kritikos About the Authors ADOLF HURWITZ was born in 1859 at Hildesheim, Germany, where he attended the Gymnasium. He studied Mathematics at the Munich Technical University and at the University of Berlin, where he took courses from Kummer, Weierstrass and Kronecker. Taking his Ph. D. under Felix Klein in Leipzig in 1880 with a thes i s on modul ar funct ions, he became Pri vatdozent at Gcitt i ngen in 1882 and became an extraordinary Professor at the University of Konigsberg, where he became acquainted with D. Hilbert and H. Minkowski, who remained lifelong friends. He was at Konigsberg until 1892 when he accepted Frobenius' chair at the Polytechnic Institute in Z~rich (E. T. H. ) where he remained the rest of his 1 i fe. |
Contents
BASIC CONCEPTS AND PROPOSITIONS 1 The Principle of Descent | 1 |
Divisibility and the Division Algorithm | 3 |
Prime Numbers | 6 |
Copyright | |
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Lectures on Number Theory Adolf Hurwitz,Nikolaos Kritikos,William C Schulz No preview available - 1985 |
Common terms and phrases
a₁ Adolf Hurwitz algorithm b₁ belongs Consequently continued fraction Corollary corresponding decomposition determine Diophantine equation divisible equation of Fermat example exist exponent form 4k+3 form f forms with discriminant greatest common divisor Hence Hint hypothesis identically implies incongruent mod incongruent solutions irrational number Jacobi symbol least common multiple lemma Let f linear congruence mathematical induction matrix mod 2k mod p-1 modulo natural number number of incongruent number of solutions odd prime pair period positive discriminant positive integer prime number primitive representations primitive root Proof Let proved Pythagorean triple quadratic residue mod r₁ real number reduced form reduced quadratic forms reduced system regular continued fraction relatively prime residue class right adjacent satisfy Show solvable square square free system of residues t+bu T₁ unimodular substitutions x₁ x²+y2 σ σ хо