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Kloosterman's sum is defined by S(u,v,n)=sum_(h)exp[(2pii(uh+vh^_))/n], (1) where h runs through a complete set of residues relatively prime to n and h^_ is defined by hh^_=1 ...

Wolfram (2002, p. 123) considered the sequence related to the Collatz problem obtained by iterating w_n={3/2w_(n-1) for w_(n-1) even; 3/2(w_(n-1)+1) for w_(n-1) odd (1) ...

A theorem which asserts that if a sequence or function behaves regularly, then some average of it behaves regularly. For example, A(x)∼x implies A_1(x)=int_0^xA(t)dt∼1/2x^2 ...

Let {A_n}_(n=0)^infty be a sequence of events occurring with a certain probability distribution, and let A be the event consisting of the occurrence of a finite number of ...

If the total group of the canonical series is divided into two parts, the difference between the number of points in each part and the double of the dimension of the complete ...

A compact manifold without boundary.

A set U has compact closure if its set closure is compact. Typically, compact closure is equivalent to the condition that U is bounded.

The discriminant of the general conic section ax_1^2+bx_2^2+cx_3^2+2fx_2x_3+2gx_1x_3+2hx_1x_2=0 is defined as Delta=|a h g; h b f; g f c|=abc+2fgh-af^2-bg^2-ch^2. If b=a and ...

An edge automorphism of a graph G is a permutation of the edges of G that sends edges with common endpoint into edges with a common endpoint. The set of all edge ...

The extended greatest common divisor of two integers m and n can be defined as the greatest common divisor GCD(m,n) of m and n which also satisfies the constraint ...