Short interval results for certain arithmetic functions

Bordellès, Olivier

doi:10.1142/s1793042118500331

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Bounding Error Terms Using That1

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Cited by 3 publications

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“…where ∆ r is the rth Hooley's divisor function (see [9] and the references therein), and using [9, Lemma 5.1], for an arbitrary fixed ε > 0, we obtain…”

Section: Bounding Error Terms Using Thatmentioning

confidence: 99%

On a sum involving the Euler function

Bordellès¹,

Dai

Heyman

et al. 2019

Journal of Number Theory

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“…where ∆ r is the rth Hooley's divisor function (see [9] and the references therein), and using [9, Lemma 5.1], for an arbitrary fixed ε > 0, we obtain…”

Section: Bounding Error Terms Using Thatmentioning

confidence: 99%

On a sum involving the Euler function

Bordellès¹,

Dai

Heyman

et al. 2019

Journal of Number Theory

Self Cite

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show abstract

Note on a paper by Bordellès, Dai, Heyman, Pan and Shparlinski

2019

Period Math Hung

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Large values of Dirichlet L-functions at zeros of a class of L-functions

2020

Can. J. Math.-J. Can. Math.

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In this paper, we are interested in obtaining large values of Dirichlet L-functions evaluated at zeros of a class of L-functions, that is, $$ \begin{align*}\max_{\substack{F(\rho)=0\\ T\leq \Im \rho \leq 2T}}L(\rho,\chi), \end{align*} $$ where $\chi $ is a primitive Dirichlet character and F belongs to a class of L-functions. The class we consider includes L-functions associated with automorphic representations of $GL(n)$ over ${\mathbb {Q}}$ .

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Short interval results for certain arithmetic functions

Abstract: Abstract. Using estimates on Hooley's ∆-function and a short interval version of the celebrated Dirichlet hyperbola principle, we derive an asymptotic formula for a class of arithmetic functions over short segments. Numerous examples are also given.

Cited by 3 publications

References 10 publications

On a sum involving the Euler function

On a sum involving the Euler function

Note on a paper by Bordellès, Dai, Heyman, Pan and Shparlinski

Large values of Dirichlet L-functions at zeros of a class of L-functions

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