• Corpus ID: 244488643

On a uniform bound for exponential sums modulo $p^m$ for Deligne polynomials

@inproceedings{Nguyen2021OnAU,
  title={On a uniform bound for exponential sums modulo \$p^m\$ for Deligne polynomials},
  author={Kien Huu Nguyen},
  year={2021}
}
  • K. Nguyen
  • Published 23 November 2021
  • Mathematics
Let f be a polynomial of degree d > 1 in n variables over Z. Let fd be the homogeneous part of degree d of f and s be the dimension of the critical locus of fd. In this paper, we prove Igusa’s conjecture for exponential sums with the exponent (n − s)/(2(d − 1)). This implies a weak solution for a recent conjecture raised by Cluckers and the author (2020) about an analogue of the results of Deligne (1974) and Katz (1999) for exponential sums over finite fields in the finite ring setting… 
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