Research interest: Algebraic number theory with emphasis on arithmetic of L-values
16. Four variable p-adic triple product L-functions and the trivial zero conjecture. (with S.Yamana)
Submitted. [pdf] (arXiv:1906.10474)
We construct the four variable p-adic triple product
L-functions attached to Hida families in the balanced
case. As an application, we prove the trivial zero conjecture for the triple product of elliptic curves.
15. Bessel periods and anticylotomic p-adic
spinor L-functions. (with Shunsuke Yamana)
Preprint. [pdf] (arXiv:1810.03231)
14. On the non-vanishing of generalized
Kato classes for elliptic curves of rank two. (with F. Castella)
Submitted. [pdf] (arXiv:1809:09066) (Revised on 03/20/19)
We prove the first cases of a conjecture of Darmon-Rotger on the non-vanishing of
13. Hida families and p-adic triple product L-functions.
American Journal of Mathematics, to appear. [pdf]
Ann. Math. Québec., 42(2018), no. 2, 215-253. [pdf]
11. Special values of anticyclotomic L-functions for modular forms. (with M. Chida)J. reine angew. Math., 741(2018), 87-131. [pdf]
10. Heegner cycles and p-adic L-functions. (with Francesc Castella)
Mathematische Annalen. 370 (2018), no. 1-2, 567-628. [pdf]
(Revised on 10/11/18) erratum.
9. Bessel periods and the non-vanishing of Yoshida lifts modulo a prime. (with Kenichi Namikawa)
Mathematische Zeitschrift, 285 (2017), no. 3, 851-878. [pdf]
8. On the anticyclotomic Iwasawa main conjecture for modular forms. (with Masataka Chida)
Compositio Mathematica, 151 (2015), no. 5, 863-897. [pdf]
(Revised on 12/20/14) erratum.
7. Special values of anticyclotomic Rankin-Selberg L-functions.
Documenta Mathematica, 19 (2014), 709-767. [pdf]
6. Eisenstein congruence on unitary groups and Iwasawa main conjectures for CM fields.
Journal of the American Mathematical Society, 27 (2014), no. 3, 753-862. [pdf]
5. On the μ-invariant of anticyclotomic p-adic L-functions for CM fields.
J. reine angew. Math., 688 (2014),
(Revised on 02/21/16)
4. The vanishing of the μ-invariant of p-adic Hecke L-functions for CM fields. (with Ashay Burungale)
IMRN, no. 5 (2013), 1014-1027. [pdf]
3. On the non-vanishing of Hecke L-values modulo p.
American Journal of Mathematics, 134 (2012), no. 6, 1503-1539. [pdf]
2. Ordinary p-adic Eisenstein series and p-adic L-functions for unitary groups.
Annales de l'Institut Fourier, 61 (2011), no. 3, 987-1059. [pdf] (Ph.D. thesis)
1. On the algebraic functional equation of Selmer group for CM fields.
Journal of Number theory, 130 (2010), 1914-1924. [pdf] (Revised on 03/05/12)
Work in progress
Derivatives of p-adic triple product L-series and p-adic heights of diagonal cycles (with S. Yamana)
Hung, Pin-Chi 洪斌哲 (NCU, May 2014)
Ph.D. thesis: Some results on the non-vanishing of central L-values
Wang, Haining (PSU, Oct. 2015, co-advised with Winnie Li)
Ph.D. thesis: Anticyclotomic Iwasawa theory for Hilbert modular forms.
Ishikawa, Isao (Kyoto U, March 2017, co-advised with Tetsushi Ito)
Ph.D. thesis: On the construction of twisted triple product p-adic L-functions
Cheng, Yao 鄭堯 (NTU, May 2018)
Ph.D. thesis: Special value formulae for triple product
L-functions and the applications
Chen, Shih-Yu 陳昰宇 (NTU, May 2018)
Ph.D. thesis: Pull-back formulas of nearly holomoprhic Saito-Kurokawa lifts