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MOTMELSUM Report Summary

Project ID: 615722
Funded under: FP7-IDEAS-ERC
Country: France

Mid-Term Report Summary - MOTMELSUM (Motivic Mellin transforms and exponential sums through non-archimedean geometry)

At this moment, we have done all the preparations needed to develop a truly motivic version of Mellin transformation, which will be the next step, and which concerns the first theme of the ERC project. These preparations consist of results in non-archimedean geometry, with a model theoretic approach. Further, new transfer principles in the context of motivic integration have been obtained with Halupczok and Gordon and are about to be submitted. Progress on the second theme of exponential sums in relation to Igusa's conjecture has been made with W. Veys, via a generalization of Igusa's Conjecture on exponential sums and with a focus on the log-canonical threshold and low powers of prime numbers. I expect further breakthrough results on this conjecture on exponential sums by the ERC Grant team in the near future.

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