Academic page


 

Research interest: Algebraic number theory with emphasis on arithmetic of L-values

 


 

Research papers


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

generalizaed Kato classes for elliptic curves of rank two. Moreover, our method also shows that the
non-vanishing of generalized Kato class implies the p-Selmer rank of ellpitic curve is two.


13. Hida families and p-adic triple product L-functions.

      American Journal of Mathematics, to appear. [pdf] (arXiv:1705.02717)


12. Inner product formula for Yoshida lifts. (with Kenichi Namikawa)

      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), 67-100. [pdf] (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)


Students


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


Itinerary


RIMS conference "Analytic, geometric and p-adic aspects of automorphic forms and L-functions", Kyoto, Jan. 20-24, 2020
Regulator 2019, Niseko, Sep. 8--13, 2019
Recent advances in the arithmetic of Galois representation, Genova, July 15-19, 2019
Iwasawa 2019, Bordeaux, June 19-29, 2019
p-adic modular forms and p-adic L-functions, Villa del Grumello, Lake Como, May 20-24, 2019
AMS Sectional Meeting, Special Session: “Advances in Iwasawa Theory”, Honolulu, March 22-24, 2019


Past trips

 


Links

MathScinet

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