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math.NT2013
Polynomials and Primes in Generalized Arithmetic Progressions (Revised Version)
Ernie Croot, Neil Lyall, Alex Rice
We provide upper bounds on the density of a symmetric generalized arithmetic progression lacking nonzero elements of the form h(n) for natural numbers n, or h(p) with p prime, for…
math.NT2013
A Purely Combinatorial Approach to Simultaneous Polynomial Recurrence Modulo 1
Ernie Croot, Neil Lyall, Alex Rice
Using purely combinatorial means we obtain results on simultaneous Diophantine approximation modulo 1 for systems of polynomials with real coefficients and no constant term.