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# Z function

In mathematics, the Z-function is a function used for studying the Riemann zeta-function along the critical line where the real part of the argument is one-half. [1]

## Analytic function

In mathematics, an analytic function is a function that is locally given by a convergent power series.

## Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

## Ernst Leonard Lindelöf

Ernst Leonard Lindelöf, (7 March 1870, Helsinki &ndash; 4 June 1946, Helsinki) was a Finnish topologist after whom Lindelöf spaces are named.

## Function (mathematics)

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

## Incomplete gamma function

In mathematics, the upper incomplete gamma function and lower incomplete gamma function are types of special functions, which arise as solutions to various mathematical problems such as certain integrals.

## Mathematics

Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change.

## Oxford University Press

Oxford University Press (OUP) is the largest university press in the world, and the second-oldest, after Cambridge University Press.

## Riemann hypothesis

In mathematics, the Riemann hypothesis, proposed by, is a conjecture that the non-trivial zeros of the Riemann zeta function all have real part 1/2.

## Riemann zeta function

The Riemann zeta function or Euler–Riemann zeta function, ζ(s), is a function of a complex variable s that analytically continues the sum of the infinite series which converges when the real part of s is greater than 1.

## Riemann–Siegel formula

In mathematics, the Riemann–Siegel formula is an asymptotic formula for the error of the approximate functional equation of the Riemann zeta function, an approximation of the zeta function by a sum of two finite Dirichlet series.

## Riemann–Siegel theta function

In mathematics, the Riemann–Siegel theta function is defined in terms of the Gamma function as \Gamma\left(\frac\right) \right) - \frac t for real values of t. Here the argument is chosen in such a way that a continuous function is obtained and \theta(0).

## Root mean square

The root mean square (abbreviated RMS or rms), also known as the quadratic mean, in statistics is a statistical measure defined as the square root of the mean of the squares of a sample.