# Selected Work of Dihua Jiang

(Some of the papers are available upon request)

### On Fourier Coefficients and Discrete Spectrum

A reciprocal probelm of the Gan-Gross-Prasad conjecture for even orthogonal groups. submitted (2017) (with Liu and Xu)

Fourier coefficients and cuspidal spectrum for symplectic groups. accepted (2017) by Symons Symposium 2016 (with Liu)

Raising nilpotent orbits in wave-front sets. Representation Theory 20 (2016), 419—450. (with Liu and Savin)

Arthur parameters and Fourier coefficients for automorphic forms on symplectic groups. Ann. Inst. Fourier (Grenoble) 66 (2016), no. 2, 477--519 (arxiv:1309.6239). (with Baiying Liu)

Fourier coefficients for automorphic forms on quasisplit classical groups. Advances in the Theory of Automorphic Forms and Their L-functions. Contemporary Math., Vol. 664, 2016, 187--208, AMS. (with Baiying Liu)

On Fourier coefficients of certain residual representations of symplectic groups. Pacific Journal of Math. Vol. 281 (2016), No. 2, 421--466 (with Baiying Liu)

On special unipotent orbits and Fourier coefficients for automorphic forms on symplectic groups. Journal of Number Theory (2015), pp. 343--389 (Rallis-JNT.pdf) (with Baiying Liu)

On Fourier coefficients of automorphic forms of GL(n). Intern. Math. Res. Notices, Vol. 2013, No. 17, pp. 4029--4071 (with Baiying Liu) (imrn13.pdf)

Poles of certain residual Eisenstein series of classical groups. Pacific J. of Math. Vol. 264, No. 1 (2013), 83--123. (with Baiying Liu and Lei Zhang) (PJM12.pdf)

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

Fourier coefficients of the residues of certain Eisenstein series of symplectic groups. preprint (2008).

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.)

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)

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 Endoscopy Theory: Construction and Characterization

Local root numbers and spectrum of the local Fourier-Jacobi descents. in preparation (with Lei Zhang and Chenyan Wu).

Local root numbers and spectrum of the local Bessel descents for unitary groups. in preparation (with Lei Zhang and Dongwen Liu).

Local root numbers and spectrum of the local descents for orthogonal groups: p-adic case. submitted (2016) (with Lei Zhang).

Periods and $(\chi,b)$-factors of cuspidal automorphic forms of symplectic groups. accepted by Israel J. of Math. (2017) (with Chenyan Wu)

On $(\chi,b)$-factors of cuspidal automorphic representations of unitary groups, II. in preparation (2015) (with Chenyan Wu)

Arthur parameters and cuspidal automorphic modules of classical groups II: Fourier-Jacobi case. in preparation, 2015 (with Lei Zhang)

Endoscopy correspondences for classical groups of hermitian type. in preparation (2014) (with Lei Zhang)

Automorphic integral transforms for classical groups II: twisted descents. submitted to Roger Howe special volume, 2016 (with Lei Zhang)

Arthur parameters and cuspidal automorphic modules of classical groups. submitted, 2015 (with Lei Zhang)

The Jacquet-Langlands correspondence via twisted descent. Int. Math.Res.Not. IMRN, 2016, no. 18, 5455—5492. (with Liu, Xu, Zhang)

On $(\chi,b)$-factors of cuspidal automorphic representations of unitary groups, I. Journal of Number Theory 161 (2016), 88--118. (with Chenyan Wu)

Automorphic integral transforms for classical groups I: endoscopy correspondences. Automorphic Forms: L-functions and related geometry: assessing the legacy of I.I. Piatetski-Shapiro. Contemporary Math., Vol. 614, 2014, AMS (Ilya.pdf)

On CAP representations for even orthogonal groups I: a correspondence of unramified representations. Chinese Annals of Math. 36B(4), 2015, 485--522. (with D. Ginzburg and D. Soudry)

On CAP representations for even orthogonal groups II: construction. preprint (2013) (with D. Ginzburg and D. Soudry)

Some conjectures on endoscopic representations in odd orthogonal groups. Nagoya Mathematical Journal (the Hiroshi Saito Memorial Volume) 208 (2012), 145--170. (saito.pdf)(with D. Ginzburg)

On correspondences between certain automorphic forms on $Sp_{4n}$ and $\widetilde{Sp}_{2n}$. Israel J. of Math. 192 (2012), 951--1008 (with D. Ginzburg and D. Soudry) (ijm11.pdf)

Construction of endoscopy transfers for classical groups Oberwolfach Notes March 2011 (Oberwolfach11.pdf)

Period integrals, poles of L-functions and liftings. SCIENCE CHINA Mathematics, Volume 53, Number 9, (2010), 2215--2238. (WangYuan.pdf) (with Ginzburg and Soudry)

Stability of cuspidal automorphic forms on $SO_{2n+1}$: vanishing periods. in preparation

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 (with Nien).

### On Langlands Local/Global Functorial Conjectures

On Tensor product L-functions and Langlands functoriality. Bull.Iranian Math. Soc. 43(2017)4, 169--189 (Shahidi 70th birthday volume).

On the local Langlands conjecture and related problems over $p$-adic local fields. Proceedings to the 6th International Congress of Chinese Mathematicians, Taipei, 2013, Adv. Lect. Math. 36, Vol. 1, 309--325, 2017. (iccm6.pdf)(with Nien, C.-F.)

Periods and relations to the Arthur and Langlands transfers. Manuscripta Math. 148 (2015), 229--233. (with Lei Zhang)

Generalized Shalika models of p-adic SO(4n) and functoriality. Israel J. Math. 195 (2013), no. 1, 135--169 (with Nien, C.-F. and Qin, Y.-J.) (IJM11.pdf)

On local descent from GL(n) to classical groups. Amer. J. of Math, Volume 134, Number 3, 2012, 767--772 (appendix to a paper by D. Prasad and D. Ramakrishnan) (with D. Soudry) (localdescent.pdf)

On certain automorphic descents to $GL_2$. IMRN 2011, no. 21, 4779--4820 (imrn10.pdf) (with D. Ginzburg and D. Soudry)

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

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

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.)

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.)

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.)

### On Automorphic L-functions and Local Factors

On inner product formula and twisted automorphic descents. in preparation (with Lei Zhang)

Bessel periods and tensor product L-functions. in preparation (with Lei Zhang)

Local theory of tensor product L-functions of classical groups: Bessel-Fourier type. in preparation (with David Soudry and Lei Zhang)

Local theory of tensor product L-functions of classical groups: Fourier-Jacobi type. in preparation (with Lei Zhang)

Towards the Jacquet conjecture on the local converse problem for p-adic GL(n). Journal of the European Mathematical Society, 17 (2015) (4), 991--1007, DOI: 10.4171/JEMS/524 (JNS13.pdf)(with C.-F. Nien and S. Stevens)

A product of tensor product L-functions for classical groups of hermitian type. Geom. Funct. Anal. 24 (2014), no. 2, 552--609. (JZhang12.pdf)(with Lei Zhang)

L-functions for symplectic groups using Fourier-Jacobi models. Arithmetic geometry and automorphic forms, 183--207, Adv. Lect. Math. (ALM), 19, Int. Press, 2011. (kudla.pdf) (with Ginzburg; Rallis; and Soudry)

Poles of L-functions and theta liftings for orthogonal groups, II. On certain L-functions, 141--158, Clay Math. Proc., 13, Amer. Math. Soc., Providence, RI, 2011 (Shahidi.pdf) (with Ginzburg and Soudry)

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)

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

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.)

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

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

### On Invariant Distributions, Local Models, and Harmonic Analysis

Vanishing of quasi-invariant generalized functions. Geometry, Number Theory, and Representation Theory, 153--168, 2013, KM Kyung Moon SA, Seoul. (jsz3.pdf) (with Binyong Sun and Chen-Bo Zhu)

Uniqueness of the Ginzburg-Rallis models: the archimedean case. Trans. Amer. Math. Soc. 363 (2011), 2763--2802. (jsz1.pdf) (with Binyong Sun and Chen-Bo Zhu)

Uniqueness of Bessel models: the archimedean case. Geom. Funct. Anal. Vol. 20 (2010) 690--709. (JSZ09.pdf) (jsz2.pdf)(with Binyong Sun and Chen-Bo Zhu)

Symplectic supercuspidal representations and related problems. SCIENCE CHINA Mathematics Vol. 53, No. 3, (2010), 533-546 (SCM10) (with Nien, C.-F. and Qin, Y.-J.)

On symplectic supercuspidal representations of GL(2n) over p-adic fields. Pacific J. of Math 245(2010)(2), 273--313 (PJM10) (with Nien, C.-F. and Qin, Y.-J.)

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

On the nonvanishing of the central value of certain L-functions: unitary groups. submitted 2017 (with Lei Zhang)

Erratum to "On the non-vanishing of the central value of the Rankin-Selberg L-functions." preprint 2015 (correction to JAMS2004) (with Ginzburg; Rallis)

Bessel models and special values of certain L-function. in preparation

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

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)

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.)

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. OSU Math. Res. Inst. Publ. 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.)

Periods of residual representations of $SO(2l)$. Manuscripta Math. 113 (2004)(3), 319--358. (mm04.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 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 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. (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)