## Number Theory Research Unit

The Number Theory Research Unit (NTRU) brings together AUB number theorists, their students, and collaborators with the aim of strengthening research and teaching in number theory, and fostering regional collaborations at the service of the field. The unit is established under the Center for Advanced Mathematical Sciences (CAMS) at the American University of Beirut, with founding members who between them have benefited from CAMS support for more than two decades now, advancing the Center's mission through international collaborations and associated activities, all the while rooting their respective research programs at AUB.

NTRU will focus on current research topics in number theory and modular forms. Unit members will host specialists in their respective research areas, organizing extended thematic programs, workshops and international conferences. Number theorists in the region will be invited to join the Unit's efforts, stimulating interest in number theory in general and sustaining focused research in fields of mutual interest. The Unit will partner with international programs to strengthen its local projects, expand its network of associated scholars, and work to secure extramural funds for collaborative projects. In due course, the Unit will, in collaboration with CAMS, announce openings for postdoctoral positions.

### Members

**Founding Members**

- Kamal Khuri-Makdisi, Professor, Department of Mathematics, AUB, Lebanon
- Wissam Raji, Professor, Department of Mathematics, AUB, Lebanon

**External Members**

- Ahmad El Guindy, Assistant Professor, Department of Mathematics, Texas A&M University, Qatar
- Alia Hamieh, Assistant Professor, Department of Mathematics, University of Northern British Columbia , Canada
- Ghaith Hiary, Associate Professor, Department of Mathematics, Ohio State University, USA

### Select Publications

- Diamantis, N., Lee M., Raji W. Rolen L. 2022. "L-Functions of Harmonic Maass Forms and a Summation Formula for Harmonic Lifts", International Mathematics Research Notices.
- Ono, K. and Raji, W. 2021. "Class numbers and self-conjugate 7-cores", Journal of Combinatorial Theory. Series A, vol.180
- Khuri-Makdisi, K., Kohnen, W., and Raji, W. 2020. "Values of L-series of Hecke eigenforms", Journal of Number Theory, vol.211, pp-28-42
- Kohnen, W. and Raji, W. 2018. "Special values of Hecke L-functions of modular forms of half-integral weight and cohomology", Research in Mathematical Sciences, vol.5, no.2
- Kohnen, W. and Raji, W. 2017. "Non-vanishing of L-functions associated to cusp forms of half-integral weight in the plus space", Research in Number Theory, vol.3, no.1
- Raji, W. 2013. "Eichler cohomology of generalized modular forms of real weights", Proceedings of the American Mathematical Society, vol.141, no.2, pp-383-392
- Mühlenbruch, T. and Raji, W. 2013. "Generalized maass wave forms", Proceedings of the American Mathematical Society, vol.141, no.4, pp-1143-1158
- Mühlenbruch, T. and Raji, W. 2013. "Eichler integrals for maass cusp forms of half-integral weight", Illinois Journal of Mathematics, vol.57, no.2, pp-445-475
- Khuri-Makdisi, K. 2012. "Moduli Interpretation of Eisenstein series", International Journal of Number Theory 8, no. 3, 715-748
- Kilford, L.J.P. and Raji, W. 2012. "On generalized modular forms supported on cuspidal and elliptic points", Ramanujan Journal, vol.27, no.3, pp-285-295
- Khuri-Makdisi, K. 2007. "Asymptotically fast group operations on Jacobians of general curves", Mathematics of Computation 76, 2213-2239
- Khuri-Makdisi, K. 2004. "Linear algebra for divisors on an algebraic curve", Mathematics of Computation 73, 333-357

### NTRU Associates

NTRU Associates are distinguished number theorists who have generously accepted to join the unit in an advisory capacity, helping Unit members (and CAMS along with them) fulfill the strategic objectives of the Unit, as they catalyze collaborative and funding opportunities within their international network. Profiles of current associates can be accessed via the links below:

- Ken Ono, Department of Mathematics, University of Virginia, USA
- Nikos Diamantis, School of Mathematical Sciences, University of Nottingham, UK
- Ozlem Imamoglu, Department of Mathematics, ETH Zurich, CH
- Michel Waldschmidt, Department of Mathematics, Université Pierre et Marie Curie (Paris 6), FR
- YoungJu Choie, Department of Mathematics, Pohang University of Science and Technology, ROK

### Upcoming Events

TBA

### Previous Events

**Nikolaos Diamantis**- Title: "L-series of weakly holomorphic forms and their values"
- Date and time: December 5, 2022 at 6:00pm (Beirut time)

**William Duke**(University of California Los Angeles UCLA, USA) - [Poster]- Title: "The Representation of Integeres by Quadratic Forms"
- Date and time: November 21, 2022 at 4:00pm (Beirut time)
- Venue: College Hall, Auditorium B1
- Recorded Lecture: https://youtu.be/_P3ouTQ9P74

**Alvaro Lozano-Robledo**(University of Connecticut, USA) - [Poster]- Title: "From Diophantus to Bitcoin: Why Are Elliptic Curves Everywhere?"
- Date and time: November 1, 2022 at 6:00pm (Beirut time)
- Recorded Lecture: https://youtu.be/JJ3s1MMDxv0

******Ghaith Hiary** (The Ohio State University, USA): Mini-course on "**The Riemann Zeta Function: Conjectures and Computations**" - [Poster]

**Ghaith Hiary**(Department of Mathematics, The Ohio State University) - [Poster]- Title: "How to Verify the Riemann Hypothesis for the First 1,000 Zeta Zeros"
- Date and time: April 12, 2022 at 4:00pm (Beirut time)
- Recorded Lecture: https://youtu.be/6fg7BJTR9Gw

**Kathrin Bringmann**(Department of Mathematics, University of Cologne) - [Poster]- Title: "Aysmptotic Properties of Modular Type Properties"
- Date and time: April 1, 2022 at 4:00pm (Beirut time)

**Michel Waldschmidt** (Department of Mathematics, Université Pierre et Marie Curie (Paris 6))- TItle: Transcendental Number Theory: Recent Results and Open Problems
- Date and time: January 18, 2022
- Recorded Lecture: https://youtu.be/1q47G3oG83Y

**Kenneth Ribet**(Department of Mathematics, University of California, Berkeley) - [Poster]- Title: "A Brief History of Fermat's Last Theorem"
- Date and time: November 8, 2021 at 7:00pm (Beirut time)
- [Presentation slides]
- Recorded Lecture: https://youtu.be/eFPUFMD4yjs

**Ken Ono**(Department of Mathematics, University of Virginia) - [Poster]- Title: "What is the Riemann Hypothesis and Why Does It Matter?"
- Date and time: October 14, 2021 at 6:00pm (Beirut time)
- Recorded Lecture: https://youtu.be/rDfCRGWVQRU

**Mathematics Summer Research Camp - June & July 2022**

- Undergraduate Students: Ali Saraeb and Maher Memneh
- Published papers: