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A "visual representation" number which is a sum of some simple function of its digits. For example, 1233 = 12^2+33^2 (1) 2661653 = 1653^2-266^2 (2) 221859 = 22^3+18^3+59^3 ...

The number of poles of an automorphic function in the closure of its fundamental region.

Let (K,|·|) be a valuated field. The valuation group G is defined to be the set G={|x|:x in K,x!=0}, with the group operation being multiplication. It is a subgroup of the ...

Let (K,|·|) be a non-Archimedean field. Its valuation ring R is defined to be R={x in K:|x|<=1}. The valuation ring has maximal ideal M={x in K:|x|<1}, and the field R/M is ...

The study of valuations which simplifies class field theory and the theory of function fields.

The quantity which a function f takes upon application to a given quantity.

A quantity which takes on the value zero is said to vanish identically, or sometimes simply to vanish. The term "vanish identically" is preferred when emphasis is needed that ...

A quantity which takes on the value zero is said to vanish. For example, the function f(z)=z^2 vanishes at the point z=0. For emphasis, the term "vanish identically" is ...

A constant sometimes called Varga's constant is defined by V=1/Lambda=9.2890254919... (OEIS A073007), where Lambda is the one-ninth constant.

The Delta-variation is a variation in which the varied path over which an integral is evaluated may end at different times than the correct path, and there may be variation ...