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1. The class number of a number field is the cardinality of the ideal class group of the field. 2. In group theory, the class number is the number of conjugacy classes of a group. 3. Class number is the number of equivalence classes of binary quadratic forms of a given discriminant. 4. The class number problem. conductor
The use of complex analysis in number theory comes later: the work of Bernhard Riemann (1859) on the zeta function is the canonical starting point; [77] Jacobi's four-square theorem (1839), which predates it, belongs to an initially different strand that has by now taken a leading role in analytic number theory (modular forms).
The David Goss Prize in Number theory, founded by the Journal of Number Theory, is awarded every two years, to mathematicians under the age of 35 for outstanding contributions to number theory. The prize is dedicated to the memory of David Goss who was the former editor in chief of the Journal of Number Theory. The current award is 10,000 USD.
Traditionally, number theory is the branch of mathematics concerned with the properties of integers and many of its open problems are easily understood even by non-mathematicians. More generally, the field has come to be concerned with a wider class of problems that arise naturally from the study of integers.
James Burton Ax (10 January 1937 – 11 June 2006) [1] was an American mathematician who made groundbreaking contributions in algebra and number theory using model theory.He shared, with Simon B. Kochen, the seventh Frank Nelson Cole Prize in Number Theory, which was awarded for a series of three joint papers [2] [3] [4] on Diophantine problems.
Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers , finite fields , and function fields .
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