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By way of analogy with the prime counting function pi(x), the notation pi_(a,b)(x) denotes the number of primes of the form ak+b less than or equal to x (Shanks 1993, pp. ...

The sequence of graphs starting with the Suzuki graph and successively taking local graphs, summarized in the following table, is known as the Suzuki tower, a name due to ...

The Dirac matrices are a class of 4×4 matrices which arise in quantum electrodynamics. There are a variety of different symbols used, and Dirac matrices are also known as ...

A quantitative measure of the simplicity of a geometric construction which reduces geometric constructions to five steps. It was devised by È. Lemoine. S_1 Place a ...

Oriented spheres in complex Euclidean three-space can be represented as lines in complex projective three-space ("Lie correspondence"), and the spheres may be thought of as ...

The pseudosquare L_p modulo the odd prime p is the least nonsquare positive integer that is congruent to 1 (mod 8) and for which the Legendre symbol (L_p/q)=1 for all odd ...

The transformation T(x) = frac(1/x) (1) = 1/x-|_1/x_|, (2) where frac(x) is the fractional part of x and |_x_| is the floor function, that takes a continued fraction ...

A plane image or pair of two-dimensional images that, when appropriately viewed using both eyes, produces an image which appears to be three-dimensional. By taking a pair of ...

In music, if a note has frequency f, integer multiples of that frequency, 2f,3f,4f and so on, are known as harmonics. As a result, the mathematical study of overlapping waves ...

The q-analog of the Pochhammer symbol defined by (a;q)_k={product_(j=0)^(k-1)(1-aq^j) if k>0; 1 if k=0; product_(j=1)^(|k|)(1-aq^(-j))^(-1) if k<0; ...