Optimality for the two-parameter quadratic sieve

Andr\'es Chirre; Emanuel Carneiro; Harald Andr\'es Helfgott; Julian Mejia-Cordero

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Optimality for the two-parameter quadratic sieve

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arxiv 2005.03162 v6 pith:M4WY4OAB submitted 2020-05-06 math.NT

Emanuel Carneiro , Andrés Chirre , Harald Andrés Helfgott , Julian Mejia-Cordero This is my paper · ORCID

classification math.NT

keywords functiongeneralquadraticsecond-ordersievetermtwo-parameterassumptions

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We study the two-parameter quadratic sieve for a general test function. We prove, under some very general assumptions, that the function considered by Barban and Vehov [BV68] and Graham [Gra78] for this problem is optimal up to and including the second-order term. We determine that second-order term explicitly.

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