Riemann–Siegel theta function

The Riemann–Siegel theta function is a special function that arises in number theory, particularly in the study of the distribution of prime numbers and the Riemann zeta function. It is named after Bernhard Riemann and Carl Ludwig Siegel, who contributed to its development and application. The Riemann–Siegel theta function is often denoted as \( \theta(x) \) and is defined in terms of a specific series that resembles the exponential function.