Upper bounds on the relative error of the singular series tail are established for smooth multivariate polynomials, with sharper decay for diagonal polynomials via exponential sum factorization and Katz's formula.
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Estimating the tail of the singular product in the multivariate Bateman-Horn conjecture
Upper bounds on the relative error of the singular series tail are established for smooth multivariate polynomials, with sharper decay for diagonal polynomials via exponential sum factorization and Katz's formula.