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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 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 &ndash; 4 June 1946) was a Finnish mathematician, who made contributions in real analysis, complex analysis and topology.

## Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

## 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 such topics as quantity, 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 is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part.

## Riemann zeta function

The Riemann zeta function or Euler–Riemann zeta function,, is a function of a complex variable s that analytically continues the sum of the Dirichlet series which converges when the real part of 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

In statistics and its applications, the root mean square (abbreviated RMS or rms) is defined as the square root of the mean square (the arithmetic mean of the squares of a set of numbers).