Research
Preprints and publications
Preprints:
(with Aleksander Horawa) Balanced triple product p-adic L-functions and Stark points (ArXiv).
Here you can look at a poster I presented at the conference in memoriam of Joël Bellaïche in June 2024 regarding this paper.
Publications:
Approximations of the balanced triple product p-adic L-function (ArXiv), Journal of Number Theory, Volume 246 (May 2023), pp. 189-226.
A brief account of this paper can be found in the poster I presented at the RTG meeting in December 2023.
Hida theory for special orders (ArXiv), Int. J. Number Theory, Volume No. 19 (March 2023), Issue No. 02, pp. 347-373.
A brief account of this paper can be found in the poster I presented at the RTG meeting in December 2023.
After this paper got accepted, I discovered I neglected a series of works that I feel must have been acknowledged in Section 4.3. Many thanks go to Kimball Martin and John Voight! These are a few papers that deal with special and, in more generality, Bass orders:
Martin - Exact double averages of twisted L-values.
Martin - The Jacquet–Langlands correspondence, Eisenstein congruences, and integral L-values in weight 2.
Martin - The basis problem revisited.
Martin, Wakatsuki - Mass formulas and Eisenstein congruences in higher rank.
Pacetti, Rodriguez-Villegas - Computing weight 2 modular forms of level p^2.
Pacetti, Sirolli - Computing ideal classes representatives in quaternion algebras.
You can find my Ph.D. thesis here (Successfully defended on September 30th, 2021).
Comments are still welcome!
The primary purpose of my thesis is to provide an algorithm for approximating the values of the balanced p-adic L-function, as constructed by Hsieh, at the limit point (2,1,1); you can read about it in Section 2. The first section is instead dedicated to the study of families of quaternionic modular forms arising from orders defined by Pizer and Hijikata-Pizer-Shemanske; the main result is a control theorem in the spirit of Hida, in which the novelty lies in the rank of the Hecke-eigenspaces being 2 (and no more 1 as in the classical case of Eichler orders). The motivation for the first section, as well as its relation with the second one, is explained in Section 3.