Revistes Catalanes amb Accés Obert (RACO)

An overlapping theorem with applications

J. Cilleruelo, G. Tenenbaum


We establish a general and optimal lower bound for the complete sum of the probabilities of $k$-intersections of $n$ events. We then describe various applications to additive and multiplicative number theory, graph theory, coding theory, study of lattice points on circles, and divisors of polynomials.

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