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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 .

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