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Hilbert's ninth problem. Hilbert's ninth problem, from the list of 23 Hilbert's problems (1900), asked to find the most general reciprocity law for the norm residues of k -th order in a general algebraic number field, where k is a power of a prime .
The following are the headers for Hilbert's 23 problems as they appeared in the 1902 translation in the Bulletin of the American Mathematical Society. [1] 1. Cantor's problem of the cardinal number of the continuum. 2. The compatibility of the arithmetical axioms. 3. The equality of the volumes of two tetrahedra of equal bases and equal altitudes.
Hilbert's ninth problem: find the most general reciprocity law for the norm residues of -th order in a general algebraic number field, where is a power of a prime. Hilbert's twelfth problem : extend the Kronecker–Weber theorem on Abelian extensions of Q {\displaystyle \mathbb {Q} } to any base number field.
Hilbert's fifteenth problem. Hilbert's sixteenth problem. Hilbert's seventeenth problem. Hilbert's eighteenth problem. Hilbert's nineteenth problem. Hilbert's twentieth problem. Hilbert's twenty-first problem. Hilbert's twenty-second problem. Hilbert's twenty-third problem.
Hilbert’s sixth problem was a proposal to expand the axiomatic method outside the existing mathematical disciplines, to physics and beyond. This expansion requires development of semantics of physics with formal analysis of the notion of physical reality that should be done. [9] Two fundamental theories capture the majority of the fundamental ...
Riemann–Hilbert problem. In mathematics, Riemann–Hilbert problems, named after Bernhard Riemann and David Hilbert, are a class of problems that arise in the study of differential equations in the complex plane. Several existence theorems for Riemann–Hilbert problems have been produced by Mark Krein, Israel Gohberg and others.
The term "reciprocity law" refers to a long line of more concrete number theoretic statements which it generalized, from the quadratic reciprocity law and the reciprocity laws of Eisenstein and Kummer to Hilbert's product formula for the norm symbol. Artin's result provided a partial solution to Hilbert's ninth problem.
Hilbert's nineteenth problem. Hilbert's nineteenth problem is one of the 23 Hilbert problems, set out in a list compiled by David Hilbert in 1900. [1] It asks whether the solutions of regular problems in the calculus of variations are always analytic. [2] Informally, and perhaps less directly, since Hilbert's concept of a " regular variational ...