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Abstract
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We obtain new bounds for short sums of isotypic trace functions associated to some sheaf
modulo prime
of bounded conductor, twisted by the Möbius function and also by the generalised divisor
function. These trace functions include Kloosterman sums and several other classical
number theoretic objects. Our bounds are nontrivial for intervals of length of at least
with an
arbitrary fixed
,
which is shorter than the required length of at least
in the case of the Möbius function and of at least
in
the case of the divisor function required in recent results of É. Fouvry, E. Kowalski
and P. Michel (2014) and E. Kowalski, P. Michel and W. Sawin (2018),
respectively.
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Keywords
Kloosterman sum, trace function, Möbius function, divisor
function
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Mathematical Subject Classification 2010
Primary: 11L05, 11N25
Secondary: 11T23
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Milestones
Received: 1 May 2018
Revised: 9 June 2019
Accepted: 26 August 2019
Published: 12 February 2020
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