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A field K is said to be an extension field (or field extension, or extension), denoted K/F, of a field F if F is a subfield of K. For example, the complex numbers are an ...

The function [x] which gives the smallest integer >=x, shown as the thick curve in the above plot. Schroeder (1991) calls the ceiling function symbols the "gallows" because ...

A doubly periodic function with periods 2omega_1 and 2omega_2 such that f(z+2omega_1)=f(z+2omega_2)=f(z), (1) which is analytic and has no singularities except for poles in ...

Quantifier elimination is the removal of all quantifiers (the universal quantifier forall and existential quantifier exists ) from a quantified system. A first-order theory ...

A dimension also called the fractal dimension, Hausdorff dimension, and Hausdorff-Besicovitch dimension in which nonintegral values are permitted. Objects whose capacity ...

A field which is complete with respect to a discrete valuation is called a local field if its field of residue classes is finite. The Hasse principle is one of the chief ...

Any square matrix T has a canonical form without any need to extend the field of its coefficients. For instance, if the entries of T are rational numbers, then so are the ...

The operator I^~ which takes a real number to the same real number I^~r=r.

Let G be a subgroup of the modular group Gamma. Then an open subset R_G of the upper half-plane H is called a fundamental region of G if 1. No two distinct points of R_G are ...

Petersson considered the absolutely converging Dirichlet L-series phi(s)=product_(p)1/(1-c(p)p^(-s)+p^(2k-1)p^(-2s)). (1) Writing the denominator as ...