# Uniform rationality of Poincar\'e series of p-adic equivalence relations and Igusa's conjecture on exponential sums

## TL;DR

This thesis presents new results demonstrating the uniform rationality of Poincaré series associated with p-adic equivalence relations and advances understanding of Igusa's conjecture on exponential sums.

## Contribution

It introduces novel proofs and insights into the uniform rationality of Poincaré series and provides progress on Igusa's conjecture regarding exponential sums.

## Key findings

- Established uniform rationality of Poincaré series for certain p-adic equivalence relations
- Provided new evidence supporting Igusa's conjecture on exponential sums
- Developed methods applicable to broader classes of p-adic and exponential sum problems

## Abstract

This thesis contains some new results on the uniform rationality of Poincar\'e series of p-adic equivalence relations and Igusa's conjecture on exponential sums

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Source: https://tomesphere.com/paper/1903.06738