E. Mehmet Kıral's Homepage

E. Mehmet Kıral's Page

Position

I am currently a Postdoctoral Researcher, working with the Mathematical Sciences Team of RIKEN AIP led by Kenichi Bannai.

Expository

Blog style mathematical vignettes on machine learning.

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

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

Author order is alphabetical in the mathematics papers.

1.	Log-Normal Multiplicative Dynamics for Stable Low-Precision Deep Learning K. Nishida, E. M. Kıral, K. Bannai, M. E. Khan, T. Möllenhoff, ICML 2026	Open Review
2.	Generating Samples to Probe Trained Models E. M. Kıral, N. Aydın, Ş. İ. Birbil	arxiv
3.	Generating Input Distributions for Explaining Portfolio Optimization Pipelines B Ataş, N. Aydın, E. M. Kıral, Ş. İ. Birbil	arxiv
4.	The Lie-Group Bayesian Learning Rule E. M. Kıral, T. Möllenhoff, E. Khan. AISTATS 2023 206:3331-3352	PMLR
5.	Subconvexity for twisted GL(3) L-functions joint with C. I. Kuan, D. Lesesvre. Acta Arithmetica 202 (2022), 281-302.	arxiv
6.	Parametrization of Kloosterman sets and SL(3)-Kloosterman sums joint with M. Nakasuji. Advances in Mathematics 403 (2022), 108392.	arxiv
7.	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): pp. 1-36.	arxiv
8.	Level Reciprocity in the twisted second moments of Rankin-Selberg L-functions joint with N. Andersen Mathematika vol. 64 no. 3 (2018): pp. 770-784.	arxiv
9.	The fifth moment of Modular L-functions joint with M. Young Journal of the European Mathematical Society (JEMS), vol. 23, no. 1 (2021): pp. 237–314	arxiv
10.	Oscillatory integrals with uniformity in parameters joint with I. Petrow, M. Young Journal de Théorie des Nombres de Bordeaux 31, no. 1 (2019): pp. 145-159.	arxiv
11.	Kloosterman sums and Fourier coefficients of Eisenstein series joint with M. Young The Ramanujan Journal, vol. 49 (2019): pp. 391-409.	arxiv
12.	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
13.	Opposite sign Kloosterman sum zeta function Mathematika, vol 62, Issue 02, (2016), pp. 406 - 429	arxiv
14.	Bounds on Sup-norms of Half Integral Weight Modular Forms Acta Arithmetica, vol. 165, no. 4 (2014): pp. 385-399	arxiv
15.	Subconvexity for Half Integral Weight L-functions. Mathematische Zeitschrift, vol. 281, Issue 3 (2015): pp. 689-722	arxiv
16.	Counting Square Discriminants joint with T. A. Hulse, C. I. Kuan, L. Lim, Journal of Number Theory, vol. 162, (2016): 255-274.	arxiv
17.	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: 13 Jul 2026