Research -- J. Hundley, SIUC

Work in Progress

Descent Construction for GSpin groups, Odd cuspidal case(Last Updated 11/5/08) Joint with Eitan Sayag. Given a cuspidal representation of GL(2n) such that the twisted exterior square $L$ function has a pole, we construct a generic cuspidal representation of GSpin(2n+1) which lifts weakly to it. A "warm up" to the general (i.e., not necessarily cuspidal) case. General odd and even cases in progress.

Draft version of the general odd case.(Last Updated 11/8/08)

Adjoint L function of SU(2,1) Modifies this construction of Ginzburg for SL(3) to accomodate quasisplit unitary groups. So far, unfolding and unramified computations only.

Published Work

• Spin $L$-functions for ${\rm GSO}\sb {10}$ and ${\rm GSO}\sb {12}$. Israel J. Math. 165 (2008), 103--132.
  
• (with D. Ginzburg) The adjoint $L$-function for ${\rm GL}\sb 5$. Electron. Res. Announc. Math. Sci. 15 (2008), 24--32.
  
• (with D. Ginzburg) On Spin $L$-functions for ${\rm GSO}\sb {10}$. J. Reine Angew. Math. 603 (2007), 183--213.
  
• Siegel zeros of Eisenstein series. Acta Arith. 126 (2007), no. 4, 341--356.
  
• (with. W.T. Gan) The spin $L$-function of quasi-split $D\sb 4$. IMRP Int. Math. Res. Pap. 2006, Art. ID 68213, 74 pp.
  
• (with D. Ginzburg) A new tower of Rankin-Selberg integrals. Electron. Res. Announc. Amer. Math. Soc. 12 (2006), 56--62 (electronic).
  
• (with D. Ginzburg) Multivariable Rankin-Selberg integrals for orthogonal groups. Int. Math. Res. Not. 2004, no. 58, 3097--3119.
  
• (with D. Ginzburg) On Certain Rankin-Selberg integrals on $GE_6.$ (To appear in Nagoya Math. J.)

"To-Do" List:

• The third integral announced in "A new tower of Rankin-Selberg integrals."
  
• The two integrals announced in "The adjoint $L$-function for ${\rm GL}\sb 5$."