Divisor functions, function fields and Matrix Integrals

Divisor functions, function fields and Matrix Integrals

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Zeev Rudnick , Tel Aviv and IAS
Fine Hall 601

I will examine some very classical questions on the statistics of divisor functions from a modern perspective of function field arithmetic and Random Matrix Theory. As a result one is able to probe new regimes in these problems, hitherto not understood even at a conjectural level.