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The conjecture is that there is a simple way to tell whether such equations have a finite or infinite number of rational solutions. More specifically, the Millennium Prize version of the conjecture is that, if the elliptic curve E has rank r , then the L -function L ( E , s ) associated with it vanishes to order r at s = 1 .
Name Coordinates Distance Diameter Data Notes Local Void: 18 h 38 m +18° : cz=2500 km/s : 60 Mpc [1]Northern Local Supervoid: 61 Mpc 104 Mpc Virgo Supercluster, Coma Supercluster, Perseus–Pisces Supercluster, Ursa Major–Lynx Supercluster, Hydra–Centaurus Supercluster, Sculptor Supercluster, Pavo–Corona Australes Supercluster form a sheet between the Northern Local Supervoid and the ...
In mathematics, the empty set or void set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. [1] Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set , while in other theories, its existence can be deduced.
Max Verstappen can cap a late night in Las Vegas with his fourth consecutive Formula 1 world championship. Verstappen enters the Las Vegas Grand Prix (1 a.m. ET Sunday, ESPN) with a 62-point lead ...
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
For example, if s=2, then 𝜁(s) is the well-known series 1 + 1/4 + 1/9 + 1/16 + …, which strangely adds up to exactly 𝜋²/6. When s is a complex number—one that looks like a+b𝑖, using ...
The elements of a polytope can be considered according to either their own dimensionality or how many dimensions "down" they are from the body. Vertex, a 0-dimensional element; Edge, a 1-dimensional element; Face, a 2-dimensional element; Cell, a 3-dimensional element; Hypercell or Teron, a 4-dimensional element; Facet, an (n-1)-dimensional element
There is a large theory of special functions which developed out of statistics and mathematical physics. A modern, abstract point of view contrasts large function spaces , which are infinite-dimensional and within which most functions are 'anonymous', with special functions picked out by properties such as symmetry , or relationship to harmonic ...