Ghaith A. Hiary

I am an associate professor in the Department of Mathematics at the Ohio State University. You can reach me at hiary.1@osu.edu or hiaryg@gmail.com.

## Publications and preprints

Note. Preparation of this material partially supported by the National Science Foundation under agreement No. DMS-1406190. The arXiv version most likely differs from published version.

## Code, data, and experiments

• An explicit van der Corput bound for $\zeta(1/2+it)$ (paper here).
• An alternative to Riemann--Siegel type formulas (paper here).
• A Deterministic $n^{1/3+o(1)}$ integer factoring algorithm (paper here).
• I've implemented the amortized complexity algorithm to compute zeta, described here. The implementation is in C++, aided by python/Sage scripts to orgnize the multi-process computation. It also includes a separate Sage program to extract "zeta data" -e.g. derivative, max,...- using band-limited interpolation. A database of (by now) ~600 million zeros near t = 10^28 (as well as smaller sets of about 200 million zeros at lower heights) has been obtained using the amortized algorithm, together with "raw data" files that allow quick extraction of further data that might be of interest. The computation took a few months on the riemann machine at U. Waterloo.
• This is a previous coding collaboration, with Jonathan Bober to implement my $T^{1/3+o(1)}$-algorithm to compute zeta, which is described here, here, and here. The implementation is in C++. It was quite useful during the implementation to constantly compare answers obtained from the C++ code with answers obtained from a basic version of the algorithm that I implemented in Mathematica back in 2009. The implementation essentially consisted of coding up the various formulas that were specified in the papers describing the algorithm.
• I'm developing a library for fast computations with Dirichlet and other L-functions. It consists of various algorithms that I have developed over the years, with a particular focus on large-scale computations. See here for an example. This is a fairly long-term project.
• Math software packages of possible interest:

SageMath (free, open-source, well-documented, comprehensive, suited for teaching and research)
CoCalc (free, open-source, well-documented, web-based cloud computing, targeted for teaching)
LMFDB (pioneering online database for L-functions)
Wolfram Alpha (web-based, especially easy to use)
Mathematica (well-documented, comperehensive, suited for teaching and research)
Matlab (well-documented, easy to learn, suited for teaching and research especially in numerical linear algebra)
R (free, open-source, well-documented, my favorite statistical package!)
Pari (free software for number theory compuations and more.)
lcalc (free software for L-function computations.)

Also, Vim is a powerful text editor, and awk is a useful scripting language in command-line.

## Past teaching

• Math 2568: Linear algebra (OSU, Spring 2020)
• Math 6111: Abstract algebra I (OSU, Autumn 2019)
• Math 3345: Foundations of Higher Mathematics (OSU, Spring 2019)
• Math 7122: Analytic Number Theory (OSU, Spring 2019)
• Math 3345: Foundations of Higher Mathematics (OSU, Autumn 2018)
• Math 2153: Calculus III (OSU, Spring 2018)
• Math 5591H & 5112: Honors Abstract Algebra (OSU, Spring 2017)
• Math 5590H & 5111: Honors Abstract Algebra (OSU, Fall 2016)
• Math 8120: Computational Number Theory (OSU, Spring 2016)
• Math 2568: Linear Algebra (OSU, Spring 2016)
• Math 5152: Introduction to Number Theory with Applications (OSU, Spring 2016)
• Math 6193: Individual Studies Numerical Linear Algebra (OSU, Spring 2016)
• Math 4193: Individual Studies (OSU, Fall 2015)
• Math 2177: Mathematical Topics for Engineers (OSU, Spring 2015)
• Math 5603: Numerical linear Algebra (OSU, Fall 2014)
• Math 2173: Engineering Mathematics B (OSU, Spring 2014)
• Math 5601: Essentials of numerical methods (OSU, Fall 2013)
• Computational Mathematics, Mechanics, and Calculus tutorials (Bristol, Fall 2012 -- Spring 2013)
• PM 340: Elementary number theory (Waterloo, Fall 2010)
• Calculus I, Calculus II, Multivariable Calculus, Linear Algebra and Differential Equations recitations (UMN, Fall 2002 -- Spring 2006)

## Seminar

OSU Number Theory Seminar