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Title:
Modular forms and their L-functions
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Abstract:
This talk will begin where my introduction to the Langlands Program from last week left off. We can associate L-functions to many families of nice modular forms. Often, these will behave like the Riemann zeta function. For example, they'll have Euler products and we expect that they satisfy a Riemann hypothesis. After examining these objects, I'll describe an ongoing investigation into half-integral weight modular forms. These are black sheep, since they *don't* satisfy a Riemann hypothesis.
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