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Optimality for the two-parameter quadratic sieve

Volume 203 / 2022

Emanuel Carneiro, Andrés Chirre, Harald Andrés Helfgott, Julián Mejía-Cordero Acta Arithmetica 203 (2022), 195-226 MSC: Primary 11N35. DOI: 10.4064/aa201018-5-1 Published online: 4 April 2022


We study the two-parameter quadratic sieve for an arbitrary smoothing function. We prove, under some very general assumptions, that the function considered by Barban and Vekhov (1968) and Graham (1978) for this problem is optimal up to and including the second-order term. We determine that second-order term explicitly.


  • Emanuel CarneiroICTP – The Abdus Salam International
    Centre for Theoretical Physics
    Strada Costiera, 11
    I-34151 Trieste, Italy
  • Andrés ChirreDepartment of Mathematical Sciences
    Norwegian University of
    Science and Technology
    NO-7491 Trondheim, Norway
  • Harald Andrés HelfgottMathematisches Institut
    Georg-August-Universität Göttingen
    Bunsenstrasse 3-5
    37073 Göttingen, Germany
  • Julián Mejía-CorderoDepartment of Mathematics
    The Ohio State University
    231 W 18th Avenue
    Columbus, OH 43210, USA

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