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The distribution of the values of a rational function modulo a big prime

Alexandru Zaharescu (2003)

Journal de théorie des nombres de Bordeaux

Given a large prime number p and a rational function r ( X ) defined over 𝔽 p = / p , we investigate the size of the set x 𝔽 p : r ˜ ( x ) > r ˜ ( x + 1 ) , where r ˜ ( x ) and r ˜ ( x + 1 ) denote the least positive representatives of r ( x ) and r ( x + 1 ) in modulo p .

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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