Distribution questions for trace functions with values in cyclotomic integers and their reductions release_5bsfskkqz5auvav3f4j7pgd4ae

by Corentin Perret-Gentil

Released as a article .

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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Date   2016-10-17
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arXiv  1610.05087v1
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