Expansion and parity

I will discuss recent work with Harald Helfgott in which we establish roughly speaking that the graph connecting nn to n±pn±p with pp a prime dividing nn is almost "locally Ramanujan". As a result we obtain improvements of results of Tao and Tao-Teravainen on logarithmic Chowla. I will discuss the main ideas in the proof and the connections with logarithmic Chowla.

Date

Affiliation

California Institute of Technology

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