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Special point on a modular curve in mathematics
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. Heegner points were
Heegner_point
German mathematician
as Heegner's.) The result is now often called the Stark–Heegner theorem. List of amateur mathematicians Stark–Heegner theorem Heegner number Heegner point
Kurt_Heegner
Topics referred to by the same term
Kurt Heegner was a German mathematician Heegner points are special points on elliptic curves The Stark–Heegner theorem identifies the imaginary quadratic
Heegner
equilibrium point Ideal point Inflection point Integral point Isolated point Generic point Heegner point Lattice hole, Lattice point Lebesgue point Midpoint
List of mathematical properties of points
List_of_mathematical_properties_of_points
British mathematician (born 1931)
conjecture). He then formulated ideas on the role of Heegner points (he was one of those reconsidering Kurt Heegner's original work on the class number one problem
Bryan_John_Birch
American mathematician
L-series of an elliptic curve evaluated at 1 to the height of a certain Heegner point. This theorem has some applications, including implying cases of the
Don_Zagier
Theory of a class of elliptic curves
integer: for example, j(Z[i]) = j(i) = 1728. Algebraic Hecke character Heegner point Hilbert's twelfth problem Lubin–Tate formal group, local fields Drinfeld
Complex_multiplication
Natural number
second kind ( 2 5 − 5 2 {\displaystyle 2^{5}-5^{2}} ), and the fourth Heegner number. Seven is the lowest natural number that cannot be represented as
7
Negative integer two units from the origin in mathematics
domain. According to the Stark–Heegner theorem, only nine negative numbers have this property, corresponding to Heegner numbers. Negative two also makes
−2
Natural number
{\displaystyle \mathrm {J_{1}} } and J 3 {\displaystyle \mathrm {J_{3}} } . 19 is a Heegner number. The James Webb Space Telescope's optical elements are in an array
19_(number)
Topics referred to by the same term
Islands, Antarctica Stark Round Barn, near Unityville, South Dakota Stark–Heegner theorem, in number theory zk-STARK (zero-knowledge Scalable Transparent
Stark
Indian mathematician (1887–1920)
{\sqrt {58}}}=396^{4}-104.000000177\dots .} This might be compared to Heegner numbers, which have class number 1 and yield similar formulae. Ramanujan's
Srinivasa_Ramanujan
In number theory, measure of non-unique factorization
and proven by Kurt Heegner, although Heegner's proof was not believed until Harold Stark gave a later proof in 1967 (see Stark–Heegner theorem). This is
Ideal_class_group
Conjecture on zeros of the zeta function
quadratic fields with class number 1 is complete, though Baker, Stark and Heegner later gave unconditional proofs of this without using the generalized Riemann
Riemann_hypothesis
Unproved conjecture in mathematics
p. 462. Zhang, Wei (2013). "The Birch–Swinnerton-Dyer conjecture and Heegner points: a survey". Current Developments in Mathematics. 2013: 169–203.
Birch and Swinnerton-Dyer conjecture
Birch_and_Swinnerton-Dyer_conjecture
Name list
musician, audio engineer and lead singer of the band Information Society Kurt Heegner (1893–1965), German mathematician Kurt Hensel (1861–1941), German mathematician
Kurt
Area of a right triangle with rational-numbered sides
1073/pnas.1216991109. PMC 3535615. PMID 23213259. Paul Monsky (1990), "Mock Heegner Points and Congruent Numbers", Mathematische Zeitschrift, 204 (1): 45–67
Congruent_number
Number divisible only by 1 and itself
explanation for this phenomenon led to the deep algebraic number theory of Heegner numbers and the class number problem. The Hardy–Littlewood conjecture F
Prime_number
and Thomas in 1974. Class numbers of imaginary quadratic fields. In 1952 Heegner published a solution to this problem. His paper was not accepted as a complete
List_of_incomplete_proofs
Compact Riemann surface of genus 3
representation theory, homology theory, Fermat's Last Theorem, and the Stark–Heegner theorem on imaginary quadratic number fields of class number one; see (Levy
Klein_quartic
packing theorems in dimensions 8 and 24 (geometry, modular forms) Stark–Heegner theorem (number theory) Subspace theorem (Diophantine approximation) Sylvester's
List_of_theorems
Varying methods used to calculate pi
the integers,[clarification needed] because there are only finitely many Heegner numbers and negative discriminants d with class number h(−d) = 1, and d
Approximations_of_pi
Coincidence in mathematics
(as is the case for most). It is a consequence of the fact that 163 is a Heegner number. There are several integers k = 2198 , 422151 , 614552 , 2508952
Mathematical_coincidence
British mathematician
collaborated with Norbert Schappacher on elucidating the biography of Kurt Heegner. In 1984 Patterson received the Whitehead Prize of the London Mathematical
Samuel_James_Patterson
Mathematical function
Maass form to E . The simultaneous generating series for the values on Heegner divisors and integrals along geodesic cycles of Klein's J-function (normalized
Harmonic_Maass_form
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