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Ramanujan's constant is the transcendental number [5], which is an almost integer: [6] = … +. This number was discovered in 1859 by the mathematician Charles Hermite. [7] In a 1975 April Fool article in Scientific American magazine, [8] "Mathematical Games" columnist Martin Gardner made the hoax claim that the number was in fact an integer, and that the Indian mathematical genius Srinivasa ...
In number theory, the Heegner theorem [1] establishes the complete list of the quadratic imaginary number fields whose rings of integers are principal ideal domains. It solves a special case of Gauss's class number problem of determining the number of imaginary quadratic fields that have a given fixed class number .
Kurt Heegner (German: [ˈheːɡnɐ]; 16 December 1893 – 2 February 1965) was a German private scholar from Berlin, who specialized in radio engineering and mathematics. He is famous for his mathematical discoveries in number theory and, in particular, the Stark–Heegner theorem .
Kurt Heegner was a German mathematician; Heegner points are special points on elliptic curves; The Stark–Heegner theorem identifies the imaginary quadratic fields of class number 1. A Heegner number is a number n such that Q(√ −n) is an imaginary quadratic field of class number 1.
That is because what enters the analytic formula for the class number is not h, the class number, on its own — but h log ε, where ε is a fundamental unit. This extra factor is hard to control. It may well be the case that class number 1 for real quadratic fields occurs infinitely often.
In mathematics, a Heegner point is a point on a modular curve that is the image of a quadratic imaginary point of the upper half-plane. They were defined by Bryan Birch and named after Kurt Heegner , who used similar ideas to prove Gauss's conjecture on imaginary quadratic fields of class number one.
For a given cation, Pauling defined [2] the electrostatic bond strength to each coordinated anion as =, where z is the cation charge and ν is the cation coordination number. A stable ionic structure is arranged to preserve local electroneutrality , so that the sum of the strengths of the electrostatic bonds to an anion equals the charge on ...
The quadratic integer ring [] of all complex numbers of the form +, where a and b are integers, is not a UFD because 6 factors as both 2×3 and as (+) (). These truly are different factorizations, because the only units in this ring are 1 and −1; thus, none of 2, 3, 1 + − 5 {\displaystyle 1+{\sqrt {-5}}} , and 1 − − 5 {\displaystyle 1 ...