Igusa's Conjecture on Exponential Sums Modulo p and p2 and the Motivic Oscillation Index

@inproceedings{Cluckers2006IgusasCO,
  title={Igusa's Conjecture on Exponential Sums Modulo p and p2 and the Motivic Oscillation Index},
  author={Raf Cluckers},
  year={2006}
}
We prove the modulo p and modulo p 2 cases of Igusa's conjecture on exponential sums. This conjecture predicts specific uniform bounds in the homogeneous polynomial case of exponential sums modulo p m when p and m vary. We introduce the motivic oscillation index of a polynomial f and prove the stronger, analogue bounds for m = 1,2 using this index instead of the original bounds. The modulo p 2 case of our bounds holds for all polynomials; the modulo p case holds for homogeneous polynomials and… CONTINUE READING

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