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Period functions of Eisenstein series and cotangent sums. May 02, 2011 (02:00 PM PDT - 03:00 PM PDT)
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Location: MSRI: Simons Auditorium
Speaker(s) Sandro Bettin
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We consider the sum $\sum_{n=1}^\infty \sigma_a(n)e^{2\pi i nz}$, showing that its period function can be analytically continued in z and has a very fast converging Taylor series in Re(z)>0. We then use these results to deduce an exact formula for the second moment of the Riemann zeta function. Moreover, we introduce a family of cotangent sums, functions over the rationals that generalize the Dedekind sum, and share with it the property of having an "almost" analytic period function.

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