Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Prof.Jean-Marc Deshouillers,Institut de Mathematique de Bordeaux, Bordeaux INP, France
Inviter:
数学所
Title:
Sums of powers: probabilistic models
Time & Venue:
2014.11.4 10:00am N210
Abstract:
In order to understand what could be expected for Waring's problem (I.e. expressing integers as sums of a bounded number of s-th powers), Erd\H{o}s and R\'{e}nyi introduced a random model for sums of s-th powers of integers. We shall present the history of the model, going through the arithmetic modification proposed with Hennecart and Landreau, as well as the latest developments (work under progress with Cilleruelo, Lambert and Plagne) concerning the possibility to represent-almost surely - any large integer as a sums of $s+1$ pseudo $s$-th powers, one of them being drastically limited in size. A general underlying theme of the lecture is: how good or bad are probabilistic models to mimic real life?
Affiliation:
Appendix:
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