The Theory of Algebraic Numbers by Harry Pollard An excellent introduction to the basics of algebraic number theory, this concise, well-written volume examines Gaussian primes; polynomials over a field; algebraic number fields; and algebraic integers and integral bases. After establishing a firm introductory foundation, the text explores the uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class...
Topics in Algebraic Number Theory. Relatively prime integers and zeta(2): The red dots are the coprime pairs of integers (x,y) with distance at most N (N = 20 in this picture) from the origin. They are connected to the origin by non-overlapping rays. The blue dots are all pairs of integers in the same disk. Their ratio tends to 1/zeta(2) = 6/pi^2 as N tends to infinity, where zeta(s) is the Riemann zeta funtion Sum_n (1/n^s). (Image by Prof. Abhinav Kumar.)
Olga Taussky-Todd (August 30, 1906, Olomouc, Moravia – October 7, 1995, Pasadena, California) was an Austrian and later Czech-American mathematician. She worked first in algebraic number theory, with a doctorate at the University of Vienna supervised by Philipp Furtwängler. She was a Fellow of the AAAS, a Noether Lecturer and a recipient of the Austrian Cross of Honour for Science and Art, 1st class (1978). She also supervised Caltech's first female Ph.D. in Math, Lorraine Foster.
Richard Dedekind born in 1831 was a German mathematician who made important contributions to abstract algebra (particularly ring theory), algebraic number theory and the foundations of the real numbers.
Emma Markovna Lehmer was a mathematician known for her work on reciprocity laws in algebraic number theory. She preferred to deal with complex number fields and integers, rather than the more abstract aspects of the theory.