E. Mehmet Kıral's Homepage

E. Mehmet Kıral's Page

Position

I am currently a Project Assistant Professor (特任講師), working at Keio University with the Mathematical Sciences Team of RIKEN AIP led by Kenichi Bannai.

Teaching

I gave a lecture series on Public Key Cryptography at RIKEN, Wako Campus as a part of iTHEMS. My Jupyter notebook lecture notes

Headshot of myself in MoMa

Personal

A place I care deeply about.
email: erenmehmetkiral@protonmail.com

Research

I like thinking about probability, entropy, thermodynamics and group actions in the context of machine learning. Also on modular forms (including half-integer weight) and their L-functions. My CV.
My Ph.D. advisor is Jeffrey Hoffstein from Brown University, and my postdoctoral mentor is Matthew Young from Texas A&M University. In Japan I was a JSPS postdoctoral fellow, working with Maki Nakasuji at Sophia University. I also was a SPDR fellow in RIKEN AIP where I made a switch to Machine Learning research.

A Haiku

With Petersson Trace,
You get more when you give less
Fewer c's, more forms

List of Publications

1. The Lie-Group Bayesian Learning Rule
joint with T. Möllenhoff, E. Khan.
AISTATS 2023 206:3331-3352
PMLR
2. Subconvexity for twisted GL(3) L-functions
joint with C. I. Kuan, D. Lesesvre.
Acta Arithmetica 202 (2022), 281-302.
arxiv
3. Parametrization of Kloosterman sets and SL(3)-Kloosterman sums
joint with M. Nakasuji.
Advances in Mathematics 403 (2022), 108392.
arxiv
4. Additive twists and a conjecture by Mazur, Rubin and Stein
joint with N. Diamantis, J. Hoffstein and M. Lee
Journal of Number Theory 209 (2020): 1-36.
arxiv
5. Level Reciprocity in the twisted second moments of Rankin-Selberg L-functions
joint with N. Andersen
Mathematika 64 (3), 770-784.
arxiv
6. The fifth moment of Modular L-functions
joint with M. Young
Accepted for Publication in the Journal of the European Mathematical Society (JEMS)
arxiv
7. Oscillatory integrals with uniformity in parameters
joint with I. Petrow, M. Young
Journal de Théorie des Nombres de Bordeaux 31, no. 1 (2019): 145-159.
arxiv
8. Kloosterman sums and Fourier coefficients of Eisenstein series
joint with M. Young
The Ramanujan Journal, 49(2), 391-409.
arxiv
9. The Voronoi formula and double Dirichlet series
joint with F. Zhou
Algebra & Number Theory vol. 10, No 10 (2016), pp. 2267-2286.
long version
arxiv
10. Opposite sign Kloosterman sum zeta function
Mathematika, vol 62, Issue 02, (2016), pp. 406 - 429
arxiv
11. Bounds on Sup-norms of Half Integral Weight Modular Forms
Acta Arithmetica, vol. 165, no. 4 (2014): pp. 385-399
arxiv
12. Subconvexity for Half Integral Weight L-functions.
Mathematische Zeitschrift, vol. 281, Issue 3 (2015): pp. 689-722
arxiv
13. Counting Square Discriminants
joint with T. A. Hulse, C. I. Kuan, L. Lim,
Journal of Number Theory, vol. 162, (2016): 255-274.
arxiv
14. The Sign of Fourier Coefficients of Half-Integral Cusp Forms
joint with T. A. Hulse, C. I. Kuan, L. Lim,
International Journal of Number Theory, vol. 8, no. 3 (2012): pp. 749-762
arxiv

Last updated: 21 January 2024