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Distribution questions for trace functions with values in cyclotomic
integers and their reductions
release_5bsfskkqz5auvav3f4j7pgd4ae
by
Corentin Perret-Gentil
Released
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.
2016
Abstract
We consider ℓ-adic trace functions over finite fields taking values in
cyclotomic integers, such as characters and exponential sums. Through ideas of
Deligne and Katz, we explore probabilistic properties of the reductions modulo
a prime ideal, exploiting especially the determination of their integral
monodromy groups. In particular, this gives a generalization of a result of
Lamzouri-Zaharescu on the distribution of short sums of the Legendre symbol
reduced modulo an integer to all multiplicative characters and to
hyper-Kloosterman sums.
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1610.05087v1
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