most citedA Montgomery-Hooley theorem for the k-fold divisor function

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math.NT2023★ 1 cited

A Montgomery-Hooley theorem for the k-fold divisor function

Tomos Parry

Let denote the -fold divisor function. For a wide range of large the expected bound $$\sum_{n\leq x\atop {n\equiv a(q)}}d_k(n)-\text { main term }\approx \sqrt {x/q…

math.NT2019

A variance for -free numbers in arithmetic progressions of given modulus

Tomos Parry

An asymptotic formula for the variance of squarefree numbers in arithmetic progressions of given modulus was obtained by Nunes (see reference [3]). We improve one of the error term…

math.NT2019

An average theorem for tuples of k-free numbers in arithmetic progressions

Tomos Parry

We obtain an asymptotic formula, in the spirit of the Montgomery-Hooley refinement of the Barban-Davenport-Halberstam Theorem, for the variance associated with tuples of k-free num…