On L-functions and the Selberg class
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The purpose of this thesis will be to explore the relationship between elliptic curves and L-functions. We will start o with a section giving some necessary defi nitions that will be used throughout the entire paper. Following this will be a section on the Selberg class of L-functions. These two chapters serve as the setup to the rest of the paper. As we will see in the Selberg section, for an L-function to be in the Selberg class it must satisfy a select few properties. So, moving from elliptic curves to modular forms we will show how the L-function associated to a modular form will actually satisfy all these conditions. Thus, the entire point of the paper can be summed up as: the L-function for a modular form belongs to the Selberg class. We will conclude with a section explaining why the Selberg Class L-functions are important.