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pro vyhledávání: '"Parry, Tomos"'
Autor:
Parry, Tomos
Nguyen has shown that on averaging over $a=1,...,q$ the 3-fold divisor function has exponent of distribution 2/3, following \cite {banks}. We follow [2] which leads to stronger bounds.
Comment: To be published in the Ramanujan journal
Comment: To be published in the Ramanujan journal
Externí odkaz:
http://arxiv.org/abs/2409.00428
Autor:
Parry, Tomos
A deep conjecture of Montgomery and Soundararajan on the distribution of prime numbers in short intervals of length $h$ says that the third moment is bounded by $\ll h^{\frac {3}{2}-c}$ for some $c>0$. There is in the literature some conditional evid
Externí odkaz:
http://arxiv.org/abs/2409.00431
Autor:
Parry, Tomos
We use the Petrow-Young [10] subconvexity bound for Dirichlet $L$-functions to show that $d_4(n)$ has exponent of distribution $4/7$ when we allow an average over $a$ mod $q$, thereby giving an equidistribution result for $d_4(n)$ which goes past the
Externí odkaz:
http://arxiv.org/abs/2404.04749
Autor:
Parry, Tomos
We give a relatively simple proof that \[ \int _0^1\left |\sum _{n\leq x}d(n)e(n\alpha )\right |d\alpha \asymp \sqrt x.\]
Externí odkaz:
http://arxiv.org/abs/2404.04747
Autor:
Parry, Tomos
Let $d_k(n)$ denote the $k$-fold divisor function. For a wide range of large $q$ the expected bound $$\sum_{n\leq x\atop {n\equiv a(q)}}d_k(n)-\text { main term }\approx \sqrt {x/q}$$ is shown to be true in an average sense -- for all $k$. This gener
Externí odkaz:
http://arxiv.org/abs/2302.11045
Akademický článek
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Autor:
Parry, Tomos
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 terms.
Comment: Published with important revisions in Journal de Th\'
Comment: Published with important revisions in Journal de Th\'
Externí odkaz:
http://arxiv.org/abs/1912.04683
Autor:
Parry, Tomos
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 numbers in arithmetic progressions.
Comment: Published in Mathematik
Comment: Published in Mathematik
Externí odkaz:
http://arxiv.org/abs/1912.03376
