Hiro-aki Narita

Department of Mathematics, Kumamoto University |

Associate Professor |

E-mail:narita``atto maaku”kumamoto-u(dt)ac(dt)jp |

**Research Intersets**

Number Theory (Particularly Automorphic forms)

**List of Publications**

1. 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.

2. 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.

3. 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.

**4.
****Irreducibility criteria for local
and global representations (joint with A. Pitale and R. Schmidt), Proceedings
of the American Mathematical Society, 141, (2013), 55-63.**

**5. ****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.**

6. 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.

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

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

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

10. 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.

11. 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.

12. 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.

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

**Preprints**

1. 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, submitted.

2. 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, preprint.

3. Real-valued automorphic functions,
preprint.

4. Modular degrees of elliptic curves and some
quotient of L-values (joint with Kousuke Sugimoto),
submitted.

Department
of Mathematics

Faculty of Science