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The Riemann zeta function is an extremely important special function of mathematics and physics that arises in definite integration and is intimately related with very deep ...

An almost integer is a number that is very close to an integer. Near-solutions to Fermat's last theorem provide a number of high-profile almost integers. In the season 7, ...

The ascending chain condition, commonly abbreviated "A.C.C.," for a partially ordered set X requires that all increasing sequences in X become eventually constant. A module M ...

Let {a_n} be a series of positive terms with a_(n+1)<=a_n. Then sum_(n=1)^(infty)a_n converges iff sum_(k=0)^infty2^ka_(2^k) converges.

The orthogonal polynomials defined by c_n^((mu))(x) = _2F_0(-n,-x;;-mu^(-1)) (1) = ((-1)^n)/(mu^n)(x-n+1)_n_1F_1(-n;x-n+1;mu), (2) where (x)_n is the Pochhammer symbol ...

A map projection which is a conformal mapping, i.e., one for which local (infinitesimal) angles on a sphere are mapped to the same angles in the projection. On maps of an ...

A polynomial Z_G(q,v) in two variables for abstract graphs. A graph with one graph vertex has Z=q. Adding a graph vertex not attached by any graph edges multiplies the Z by ...

An E_8 polytope is a polytope having the symmetry of the exceptional simple Lie groups E_8 of dimension 248. There are 255 uniform polytopes with E_8 symmetry in 8 ...

The Fermat quotient for a number a and a prime base p is defined as q_p(a)=(a^(p-1)-1)/p. (1) If pab, then q_p(ab) = q_p(a)+q_p(b) (2) q_p(p+/-1) = ∓1 (3) (mod p), where the ...

A place nu of a number field k is an isomorphism class of field maps k onto a dense subfield of a nondiscrete locally compact field k_nu. In the function field case, let F be ...