Open Access
Class Number One Problems
Elijah Bunnell
- 24 Apr 2009
About: The article was published on 24 Apr 2009. and is currently open access. The article focuses on the topics: Stark–Heegner theorem & Heegner number.
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References
A classical introduction to modern number theory
Kenneth Ireland,Michael Rosen +1 more
- 01 Jan 1982
TL;DR: This second edition has been corrected and contains two new chapters which provide a complete proof of the Mordell-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curve.
•Book
Primes of the Form x2 + ny2: Fermat, Class Field Theory, and Complex Multiplication
David A. Cox
- 01 Jan 1989
Abstract: FROM FERMAT TO GAUSS. Fermat, Euler and Quadratic Reciprocity. Lagrange, Legendre and Quadratic Forms. Gauss, Composition and Genera. Cubic and Biquadratic Reciprocity. CLASS FIELD THEORY. The Hilbert Class Field and p = x 2 + ny 2 . The Hilbert Class Field and Genus Theory. Orders in Imaginary Quadratic Fields. Class Fields Theory and the Cebotarev Density Theorem. Ring Class Field and p = x 2 + ny 2 . COMPLEX MULTIPLICATION. Elliptic Functions and Complex Multiplication. Modular Functions and Ring Class Fields. Modular Functions and Singular j--Invariants. The Class Equation. Ellpitic Curves. References. Index.
669
Linear forms in the logarithms of algebraic numbers
TL;DR: Gelfond as discussed by the authors showed that the logarithm of a linear algebraic number to an algebraic base, other than 0 or 1, is either rational or transcendental and thereby solved the famous seventh problem of Hilbert.
392
Gauss’ class number problem for imaginary quadratic fields
TL;DR: The Disquisitiones also contain tables of binary quadratic forms with small class numbers as mentioned in this paper, which is a result first proved by Heilbronn [H] in 1934.
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