Research Interests

Automorphic forms, in particular, Jacobi forms and Hilbert modular forms. General reciprocity, Hecke Gauss sums. Hilbert Theory modular groups. Weil representations.

Publications

Research Monographs

  1. Boylan, H. Jacobi forms, finite quadratic modules and Weil representations over number fields. volume 2130 of Lecture Notes in Mathematics (Monograph). Springer International Publishing, Switzerland (2015).

Articles

  1. Boylan, H., Skoruppa, N.-P. Explicit formulas for Hecke Gauss sums in quadratic number fields. Abh. Math. Semin. Univ. Hambg. 80, 213-226 (2010).
  2. Boylan, H., Skoruppa N.-P. Linear characters of SL_2 over Dedekind domains. J. Algebra 373 120-129 (2013) arXiv:1205.4288 [math.NT]
  3. Boylan, H., Skoruppa, N.-P. A quick proof of reciprocity for Hecke Gauss sums. J. Number Theory 133 110–114 (2013).
  4. Boylan, H. Finite quadratic modules over number fields and their associated Weil representations RIMS Kôkyûroku (Proc. RIMS) 1871 125-136 (2013).
  5. Boylan, H., Skoruppa, N.-P., Zhou, H. Counting zeros in quaternion algebras using Jacobi forms Transactions of AMS, Volume 371 (9), 6487-6509 (2019).
  6. Boylan, H., Skoruppa, N.-P., A classical approach to relative quadratic extensions arXiv:2208.03515 [math.NT] (preprint, 2022) .
  7. Boylan, H., Skoruppa, N.-P., Jacobi Forms of Lattice Index I. Basic Theory arXiv:2309.04738 [math.NT] (preprint, 2023).
  8. Boylan, H., Jacobi-Eisenstein series over number fields Journal of Number Theory, Volume 248, Pages 54-77 (2023).
  9. Boylan, H., The adjoint of the nullwert map on Jacobi forms of lattice index. (submitted for publication, 2023).