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Dirichlet ... -functions are important in number theory. For example, ... -functions are used to prove Dirichlet's theorem, which states that the arithmetic progression ... ( ... ) contains infinitely many primes, provided ... and ... are relatively prime. The zeros of ... -functions can even be used to count how many primes less than ... there are in arithmetic progressions. This Demonstration graphs Dirichlet ... -functions along the line ... in the complex plane (the so-called "critical line"), and highlights the zeros that are encountered. Zeros occur where the real part (blue graph) and the imaginary part (red graph) are simultaneously 0.
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