Hiro-aki
Narita

Department
of Mathematics, Faculty of Science and Engineering, Waseda University |

Professor |

E-mail:hnarita``atto
maaku”waseda(dt)jp |

**Research Intersets**

Number Theory (Particularly Automorphic
forms)

**List of Publications**

1. Jacquet-Langlands-Shimizu
correspondence for theta lifts to GSp(2) and its inner forms II: an explicit formula for Bessel
periods and non-vanishing of theta lifts, Journal of the Mathematical Society
of Japan, 73 (2021) 125-159.

2. Modular
degrees of elliptic curves and some quotient of L-values (joint with Kousuke
Sugimoto), Tokyo Journal of Mathematics, 43 No.2 (2020) 279-293.

3. An explicit construction
of non-tempered cusp forms on O(1,8n+1) (joint with Yingkun Li and Ameya
Pitale), Annales Math. Quebec, 44 (2) (2020) 349-384.

4. Jacquet-Langlands-Shimizu
correspondence for theta lifts to GSp(2) and its inner forms I: an explicit functorial correspondence,
with an appendix by Ralf Schmidt, Journal of the Mathematical Society of Japan,
69 (2017), 1443-1474.

5. Lifting to GL(2) over a division quaternion algebra and an explicit
construction of CAP representations (joint with Masanori Muto and Ameya Pitale), Nagoya Mathematical Journal, 222, issue
01, (2016), 137-185.

6. Fourier
expansion of Arakawa lifting II: Relation with central L-values (joint with
Atsushi Murase), International Journal of Mathematics, 27, No. 1, (2016), 32
pages.

7. Bessel
periods of theta lifts to GSp(1,1) and central values
of some convolution type L-functions, Automorphic forms, Research in Number
Theory from Oman, Springer Proceedings in Mathematics and Statistics (2014),
179-191.

**8. ****Irreducibility
criteria for local and global representations (joint with A. Pitale and R.
Schmidt), Proceedings of the American Mathematical Society, **

**141, (2013), 55-63.**

**9. ****Some vector-valued singular automorphic forms on
U(2,2) and their restriction to Sp(1,1)
(joint with Atsuo Yamauchi), International Journal of Mathematics, 23, No. 10,
(2012), 27 pages.**

10. Fourier expansion of Arakawa lifting I: An explicit formula and examples of non-vanishing lifts (joint with Atsushi Murase), Israel Journal of Mathematics, 187, (2012), 317-369.

11. Commutation
relations of Hecke operators for Arakawa lifting (joint with Atsushi Murase),
Tohoku Mathematical Journal, **60**, (2008), 227-251.

12. Theta
lifting from elliptic cusp forms to automorphic forms on Sp(1,q), Mathematische Zeitschrift, **259**, (2008), 591-615.

13. Fourier-Jacobi
expansion of automorphic forms on Sp(1,q) generating quaternionic discrete series, Journal of
Functional Analysis, **239**, (2006), 638-682.

14. On certain
automorphic forms of Sp(1,q) (Arakawa's results and
recent progress), Proceedings of the conference in memory of Tsuneo Arakawa,
Automorphic forms and zeta functions, World Scientific (2006), 314-333.

15. Fourier
expansion of holomorphic modular forms on classical Lie groups of tube type
along the minimal parabolic subgroup, Abhandlungen aus dem Mathematischen Seminar der Universitaet
Hamburg, **74**, (2004), 253-279.

16. Fourier
expansion of holomorphic Siegel modular forms of genus n along the minimal
parabolic subgroup, Journal of Mathematical Sciences, the University of Tokyo, **10**,
(2003), 311-353.

17. Fourier
expansion of holomorphic Siegel modular forms with respect to the minimal
parabolic subgroup, Mathematische Zeitschrift,
**231**,
(1999), 557-588.

**Preprints**

Real-valued
automorphic functions, submitted.

Fourier-Jacobi
expansion of cusp forms on Sp(2,R), arXive:2111.00756

Department of Mathematics

Faculty of Science and Engineering