Restriction estimates for the paraboloid over finite fields
msra(2010)
摘要
We prove certain endpoint restriction estimates for the paraboloid over
finite fields in three and higher dimensions. Working in the bilinear setting,
we are able to pass from estimates for characteristic functions to estimates
for general functions while avoiding the extra logarithmic power of the field
size which is introduced by the dyadic pigeonhole approach. This allows us to
remove logarithmic factors from the estimates obtained by Mockenhaupt and Tao
in three dimensions and those obtained by Iosevich and Koh in higher
dimensions.
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关键词
three dimensions,finite field,generating function,characteristic function
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