Displaying similar documents to “Some extensions and refinements of a theorem of Sylvester”

Diophantine equations after Fermat’s last theorem

Samir Siksek (2009)

Journal de Théorie des Nombres de Bordeaux

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These are expository notes that accompany my talk at the 25th Journées Arithmétiques, July 2–6, 2007, Edinburgh, Scotland. I aim to shed light on the following two questions: Given a Diophantine equation, what information can be obtained by following the strategy of Wiles’ proof of Fermat’s Last Theorem? ...

A note on arithmetic Diophantine series

Alexander E. Patkowski (2021)

Czechoslovak Mathematical Journal

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We consider an asymptotic analysis for series related to the work of Hardy and Littlewood (1923) on Diophantine approximation, as well as Davenport. In particular, we expand on ideas from some previous work on arithmetic series and the RH. To accomplish this, Mellin inversion is applied to certain infinite series over arithmetic functions to apply Cauchy's residue theorem, and then the remainder of terms is estimated according to the assumption of the RH. In the last section, we use...