Corentin Perret-Gentil

Number theory

Papers

1. Gaussian distribution of short sums of trace functions over finite fields (42 pages).
Published in Mathematical Proceedings of the Cambridge Philosophical Society 163(3), November 2017.
2. Integral monodromy groups of Kloosterman sheaves (27 pages).
Published in Mathematika 64(3), June 2018.
3. Distribution questions for trace functions with values in cyclotomic integers and their reductions (48 pages).
Published in Transactions of the AMS 371(7), April 2019.
4. Exponential sums and the large sieve (28 pages).
Published in International Mathematics Research Notices, August 2018.
5. Joint distribution of inverses in matrix groups over finite fields (16 pages).
Submitted, 2018.
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).
2018.
7. The average number of subgroups of elliptic curves over finite fields (39 pages).
Submitted, 2018.
8. A note on the dimension of the largest simple Hecke submodule (11 pages) with Sandro Bettin and Maksym Radziwiłł.
Published in International Mathematics Research Notices, December 2018.
9. Roots of $L$-functions of characters over function fields, generic linear independence and biases (40 pages).
Submitted, 2019.

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

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.

Some miscellaneous projects

(with possibly less math than the above; in no particular order)

Last updated: June 2019