Corentin Perret-Gentil

### Research

#### Papers

1. Gaussian distribution of short sums of trace functions over finite fields (42 pages, PDF)
Mathematical Proceedings of the Cambridge Philosophical Society 163(3), November 2017.
2. Integral monodromy groups of Kloosterman sheaves (27 pages, PDF)
Mathematika 64(3), June 2018.
3. Distribution questions for trace functions with values in cyclotomic integers and their reductions (48 pages, PDF)
Transactions of the AMS 371(7), April 2019.
4. Exponential sums and the large sieve (28 pages, PDF)
International Mathematics Research Notices, August 2018.
5. Joint distribution of inverses in matrix groups over finite fields (16 pages, PDF)
Research in Number Theory 5(4), November 2019.
6. Random invariant generation of $\SL_{n}(\F_q)$ and $\Sp_{2n}(\F_q)$ by a full unipotent Jordan block and a generic element (12 pages, PDF)
2018.
7. The average number of subgroups of elliptic curves over finite fields (39 pages, PDF)
Quarterly Journal of Mathematics, July 2020.
8. A note on the dimension of the largest simple Hecke submodule (11 pages, PDF) with Sandro Bettin and Maksym Radziwiłł
International Mathematics Research Notices, December 2018.
9. Roots of $L$-functions of characters over function fields, generic linear independence and biases (41 pages, PDF)
Algebra & Number Theory, 2020.

In chronological order of writing. These may slightly differ from the published versions.

With Daedalean and the European Union Aviation Safety Agency's AI task force:

#### PhD thesis

Probabilistic aspects of short sums of trace functions over finite fields (170 pages), ETH Zürich, 2016, updated version.

#### Student projects

These are student projects; no claim of originality or correctness.

Last updated: May 2021