Research -- J. Hundley, SIUC
Work in Progress
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The egut project (ongoing programming project).
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Descent Construction for GSpin Groups (Joint with E. Sayag):
- Holomorphicity of adjoint L functions and ratios of Dedekind zeta functions. Show that the adjoint L function of a cuspidal representation of GL(3) or U(2,1) can not have a pole using the integral representation in $G_2$ given below.
Show the same about a ratio of Dedekind zeta functions attached to a cubic extension of number fields using the integral representation due to Jiang and Rallis. Methods should extend to
GL(4) and GL(5).
- Doubling integral for $G_2$ (joint with D. Ginzburg)
- Survey of integral representations in the exceptional groups (long term, joint with D. Ginzburg)
Recently completed
Published Work
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(with E. Sayag)
Descent construction for GSpin groups: main results and applications. Electron. Res. Announc. Math. Sci. 16 (2009), 30Ð36.
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(with D. Ginzburg) On certain Rankin-Selberg integrals on $GE_6.$ . Nagoya Math. J. 191 (2008), 21Ð78.
- 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.
"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 ${\rm GL}\sb 5$."