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MODULAR FORMS of WEIGHT DEFINED on PRODUCTS of P Ams

MODULAR FORMS of WEIGHT DEFINED on PRODUCTS of P Ams

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Skinner thank you um this is going to use the chalkboard Sara will be hopefully it's fairly slowly paced and I don't expect to to be too comprehensive either basically I'm going to focus on one example so I'm going to start with the following series which a certainly interest number theorists at least since the days of Euler and part of the interest comes from the fact that can also be written as a product over the primes it's more or less reflects the unique factorization of integers and though it might not have bothered boiler too much I mean we can really only perhaps talk about that for the rest being larger than one although following Riemann we now call this the zeta function and think of it as a function in the complex plane and which case all of this makes sense for the real part of s one well Oilers first probably great achievement around I think 1735 was a solution of the Basel problem which was to show that the sum of the reciprocals o

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