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Li's criterion states that the Riemann hypothesis is equivalent to the statement that, for lambda_n=1/((n-1)!)(d^n)/(ds^n)[s^(n-1)lnxi(s)]|_(s=1), (1) where xi(s) is the ...

A test used to determine the statistical significance of an observation. Two main types of error can occur: 1. A type I error occurs when a false negative result is obtained ...

(Bailey 1935, p. 25), where _7F_6(a_1,...,a_7;b_1,...,b_6) and _4F_3(a_1,...,a_4;b_1,b_2,b_3) are generalized hypergeometric functions with argument z=1 and Gamma(z) is the ...

Consider the inequality sigma(n)<e^gammanlnlnn for integer n>1, where sigma(n) is the divisor function and gamma is the Euler-Mascheroni constant. This holds for 7, 11, 13, ...

Voronin (1975) proved the remarkable analytical property of the Riemann zeta function zeta(s) that, roughly speaking, any nonvanishing analytic function can be approximated ...

An alpha value is a number 0<=alpha<=1 such that P(z>=z_(observed))<=alpha is considered "significant," where P is a P-value.

The probability that a variate would assume a value greater than or equal to the observed value strictly by chance: P(z>=z_(observed)).

A p-form alpha is indecomposable if it cannot be written as the wedge product of one-forms alpha=beta_1 ^ ... ^ beta_p. A p-form that can be written as such a product is ...

Percolation, the fundamental notion at the heart of percolation theory, is a difficult idea to define precisely though it is quite easy to describe qualitatively. From the ...

One of Cantor's ordinal numbers omega, omega+1, omega+2, ..., omega+omega, omega+omega+1, ... which is "larger" than any whole number.