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Abstract
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We study the incrementation of the lower asymptotic density
compared
with
, where
is a specific set and
is arbitrary. Ruzsa proved
optimal inequalities of
for
being a set of prime powers or integer powers. We generalize
Ruzsa’s result to sets of polynomial values. Moreover, for
with a positive leading
coefficient and
, we
prove that
if and only
if
is not identically
zero modulo any
.
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Keywords
sumsets, essential components, circle method
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Mathematical Subject Classification
Primary: 11B13, 11P55
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Milestones
Received: 28 February 2022
Revised: 13 June 2022
Accepted: 29 June 2022
Published: 15 October 2022
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