Selected Work of Dihua Jiang

(Some of the papers are available upon request)

On Langlands Local/Global Functorial Conjectures

  • On certain descent maps to $GL_2$
    submitted (2009) (with D. Ginzburg and D. Soudry)

  • On the Langlands Functoriality: constructive methods.
    ICTP summer school lecture notes, 2007. in preparation

  • On the Langlands functoriality for automorphic forms.
    Advances in Math (China) Vol. 37, 2008, No. 2, 129--152. (amc08.pdf)

  • On the fundamental automorphic $L$-functions of SO(2n+1).
    IMRN Volume 2006, Article ID 64069, 1--26 (imrn06.pdf)

  • Endoscopy and local gamma factors. in preparation.

  • Endoscopy and poles of L-functions
    International conference on number theory and arithmetic geometry
    in honour of John H. Coates on his 60th Birthday (J. Coates) 2005 (coates.pdf)

  • On local gamma factors.
    Arithmetic Geometry and Number Theory (ws06.pdf).
    Series on Number Teory and Applications, Vol 1, 1--28, 2006, World Scientific

  • On Langlands conjectures in the theory of automorphic forms.
    Proc. of the 2nd International Congress of Chinese Mathematicians (Taipei) 2001, 217--232
    New Studies in Advanced Mathematics No. 4, International Press 2004 (iccm2.pdf)

  • Generic representations and local Langlands reciprocity law for p-adic $SO(2n+1)$.
    Contributions to automorphic forms, geometry, and number theory, 457--519,
    Johns Hopkins Univ. Press, Baltimore, MD, 2004. (Shlika17.pdf) (with Soudry, D.)

  • Local converse theorem for SO(2n+1) and applications.
    Ann. of Math. 157(2003), 743--806 (am03.pdf) (with Soudry, D.)

  • Periods and liftings: from $G\sb 2$ to $C\sb 3$.
    Israel J. of Math. 123 (2001), 29--59. (math-review) (ijm01.pdf) (with Ginzburg, D.)

  • A Siegel-Weil identity for $G\sb 2$ and poles of L-functions.
    J. of Number Theory 82 (2000), 256--287. (jnt00.pdf) (with Ginzburg, D.)

    On Square Integrable Automorphic Representations: Arthur Conjectures

  • On certain CAP automorphic forms of symplectic groups
    in preparation (with D. Ginzburg and D. Soudry)

  • Fourier coefficients of automorphic forms and transfers
    preprint (2009) (with D. Ginzburg and D. Soudry)

  • On certain CAP automorphic forms of orthogonal groups
    preprint (2009) (with D. Ginzburg and D. Soudry)

  • Stability of cuspidal automorphic forms on $SO_{2n+1}$: vanishing periods
    in preparation (with D. Ginzburg)

  • Poles of certain automorphic L-functions
    Lecture Notes at Goldfeld's birthday conference 2007

  • On the discrete spectrum of automorphic forms.
    Proceedings of the 4th International Congress of Chinese Mathematicians, Vol. I, 165-188, Hangzhou, December, 2007 (lecture)(iccm4.pdf)

  • On multiplicity one theorem for generic cuspidal automorphic representations of $GSp(4)$.
    Pacific J. of Math. Vol. 229, No. 2, Feb 2007 381--388 (with Soudry, D.) (pjm07.pdf)

  • On the genericity of cuspidal automorphic forms of $SO_{2n+1}$, II.
    Compositio Math. Volume 143 Part 3 (May 2007), 721--748 (cm07.pdf) (with Soudry, D.)

  • On the genericity of cuspidal automorphic forms of $SO_{2n+1}$.
    J. Reine Angew. Math. 604 (2007), 187--209. (crelle07.pdf) (with Soudry, D.)

  • Cubic unipotent Arthur parameters and multiplicities of square integrable automorphic forms.
    Invent. Math. 149 (2002), no. 2, 225--265. (im02.pdf) (with Gan, W. T.; Gurevich, N.)

  • On CAP automorphic representations of a aplit group of type $D_4$.
    J. Reine Angew. Math. 552 (2002), 179--211. (crelle02.pdf) (with Ginzburg, D.; Rallis, S.)

    On Theta Correspondences and Howe Duality

  • Poles of L-functions and theta liftings for orthogonal groups.
    Journal of the Institute of Math. of Jussieu (2009) 8(4), 693--741. (jimj.pdf) (with Ginzburg and Soudry)

  • Poles of L-functions and theta liftings for orthogonal groups, II.
    accepted by the Shahidi's birthday conference volume 2008.(Shahidi.pdf) (with Ginzburg and Soudry)

    On Eisenstein Series and the Residues

  • Fourier coefficients of the residues of certain Eisenstein series of symplectic groups.
    preprint (2008) (with Ginzburg, D.)

  • Models for certain residual representations of unitary groups
    The AMS series Contemporary Mathematics(IMCP/CONM) for Stephen Gelbart, Vol 488, 125--146, 2009. (Gelbart.pdf)(with Ginzburg, D. and Rallis, S.)
    .

  • Residues of Eisenstein series and related problems
    Eisenstein Series and Applications. Progress in Math, 258, 187--204, 2008. (pm08.pdf)

  • Residues of Eisenstein series and generalized Shalika models for SO(4n)
    J. of the Ramanujan Math. Soc. 22, No. 2 (2007) 1--33 (jrms07.pdf)(with Qin, Y.-J.)

  • Periods of residual representations of $SO(2l)$.
    Manuscripta Math. 113 (2004)(3), 319--358. (mm04.pdf) (with Ginzburg, D.; Rallis, S.)

  • The first term identities for Eisenstein series.
    J. Number Theory 70 (1998), no. 1, 67--98. (jnt98.pdf)

    On Relative Trace Formula

  • A relative Kuznietsov trace formula on $G\sb 2$.
    Manuscripta Math. 99 (1999), no. 3, 411--423. (mm99.pdf) (with Mao, Z.; Rallis, S.)

    On Local Models of Representations and Related Problems

  • Uniqueness of the Ginzburg-Rallis models: the archimedean case.
    submitted 2008 (jsz1.pdf) (with Binyong Sun and Chen-Bo Zhu)

  • Uniqueness of Bessel models: the archimedean case
    submitted 2009 (jsz2.pdf)(with Binyong Sun and Chen-Bo Zhu)

  • Local Shalika models and functoriality
    Manuscripta Math. 127, 187-217 (2008) (mm08.pdf) (onlinefirst) (with Nien, C.-F. and Qin, Y.-J.)

  • On symplectic supercuspidal representations of GL(2n) over p-adic fields.
    accepted by Pacific J. of Math 2009 (pjm.pdf) (with Nien, C.-F. and Qin, Y.-J.)

  • Symplectic Supercuspidal Representations and Related Problems.
    submitted to Sciences in China, Special volume in honor of Professor Yang Lo in occasion of of his seventieth birthday
    (with Nien, C.-F. and Qin, Y.-J.)

  • Generalized Shalika models and stability.
    in preparation (2009) (with Nien, C.-F. and Qin, Y.-J.)

    On Periods of Automorphic Forms: Conjectures of the Gross-Prasad Type

  • Period integrals, poles of L-functions and liftings
    in preparation (2009) (with Ginzburg and Soudry)

  • Periods of automorphic forms.
    Proceedings of the International Conference on Complex Geometry and Related Fields.
    Studies in Advanced Mathematics, Vol 39, 2007, 125--148. AMS/IP. (ecnu.pdf)

  • Nonvanishing of the central value of the Rankin-Selberg L-functions
    RIMS Kokyuroku 1468, Automorphic Forms and Automorphic L-functions, Feb, 2006. (rims05.pdf)

  • On the non-vanishing of the central value of the Rankin-Selberg L-functions II.
    Automorphic Representations, L-Functions and Applications: Progress and Prospects.
    Ohio State University Mathematical Research Institute Publications 11. (OSU 11)
    2005. (Rallis.pdf) (with Ginzburg, D.; Rallis, S.)

  • On the non-vanishing of the central value of the Rankin-Selberg L-functions.
    Journal of AMS. 17 (2004), 679-722. (jams04.pdf) (with Ginzburg, D.; Rallis, S.)

  • On Jacquet's conjecture: split period case.
    Internat. Math. Res. Notices (2001), no. 3, 145--163. (imrn01.pdf)

  • Nonvanishing of the central critical value of the third symmetric power $L$-functions.
    Forum Math. 13 (2001), 109--132. (math-review) (fm01.pdf)(with Ginzburg, D.; Rallis, S.)

  • Nonvanishing of the central critical value of the triple product $L$-functions.
    Internat. Math. Res. Notices 1998, no. 2, 73--84. (imrn98.pdf)

  • $G\sb 2$-periods and residual representations.
    J. Reine Angew. Math. 497 (1998), 17--46. (crelle98.pdf)

  • An Approacch to a Conjecture of Jacquet.
    Proceedings of the Seattle conference, July 1997. (Seattle97)

    On Automorphic Forms, Shimura Varieties, and Arithmetic Problems

  • Periods and distribution of cycles on Hilbert modular varieties.
    Pure and Applied Mathematics Quarterly, 2(2006)(1), 221--279.
    Special Issue in homor of John H. Coates (pamq06.pdf) (with Li, Jianshu; Zhang, Shouwu)

  • Arithmeticity of discrete subgroups and automorphic forms.
    Geom. Funct. Anal. 8 (1998), no. 3, 586--605. (gafa98.pdf)(with Piatetski-Shapiro, I.)

  • Fourier coefficients of Eisenstein series of the exceptional group of type $G\sb 2$.
    Pacific J. Math. 181 (1997), no. 2, 281--314. (pjm97.pdf)(with Rallis, S.)

  • Theorems on norm groups and genera. (Chinese)
    Northeast. Math. J. 5 (1989), no. 3, 255--258 (math-review)

  • The structure of the Grothendieck groups of almost unimodular quadratic lattices. (Chinese)
    Chinese Ann. Math. Ser. A 10 (1989), no. 2, 229--24 (math-review)

    On Integral Constructions of Automorphic L-functions

  • L-functions for symplectic groups using Fourier-Jacobi models.
    to appear in Kudla's volume (2009) (kudla.pdf) (with Ginzburg; Rallis; and Soudry)

  • Degree $16$ standard $L$-function of GSp(2) x GSp(2).
    Mem. Amer. Math. Soc. 123 (1996), no. 588 (196pp) (math-review) (mams96.pdf)

  • Degree $16$ standard $L$-function of GSp(2) x GSp(2).
    PhD. Dissertation, 1994, The Ohio State University