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The Diophantine Equation X³ = u+v over Real Quadratic Fields

Takaaki Kagawa (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

Let k be a real quadratic field and let k and k × be the ring of integers and the group of units, respectively. A method of solving the Diophantine equation X³ = u+v ( X k , u , v k × ) is developed.

The divisor problem for binary cubic forms

Tim Browning (2011)

Journal de Théorie des Nombres de Bordeaux

We investigate the average order of the divisor function at values of binary cubic forms that are reducible over and discuss some applications.

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