Dirichlet L-functions are complex functions that generalize the Riemann zeta function. They are associated with Dirichlet characters, which are periodic arithmetic functions that take values in the complex numbers. These functions play a crucial role in number theory, particularly in understanding the distribution of prime numbers in arithmetic progressions. The L-functions are defined for a Dirichlet character \chi and a complex variable s . They converge for \textRe(s) > 1 and can be analytically continued to other values of s . The study of Dirichlet L-functions is essential in the proof of the Dirichlet's theorem on arithmetic progressions, which states that there are infinitely many primes in certain sequences.