Stephen S. Kudla


Here are some, mostly recent, papers:

1. Some extensions of the Siegel-Weil formula, pdf.
This article is based on a lecture given at RIMS, Kyoto in January of 1992.

2. Notes on the local theta correspondence, pdf.
Notes from 10 lectures given at the European School on Group Theory in September 1996.

3. Arithmetic Hirzebruch Zagier cycles, (joint with Michael Rapoport), J. reine angew. Math., 515 (1999), 155--244 pdf.

4. Cycles on Siegel 3-folds and derivatives of Eisenstein series, (joint with Michael Rapoport), Annales Ecole. Norm. Sup. 33 (2000), 695--756. pdf.

5. Derivatives of Eisenstein series and generating functions for arithmetic cycles, S\'eminaire Bourbaki, 52 ann\'ee,
1999--2000, no 876, Ast\'erisque, 276, (2002), 341--368. pdf.
Lecture in Seminar Bourbaki, June 2000.

6. Height pairings on Shimura curves and p-adic uniformization,(joint with Michael Rapoport), Inventiones Math. 142 (2000), 153--223. pdf.

7. Derivatives of Eisenstein series and Faltings heights, (joint with Michael Rapoport and Tonghai Yang), Compositio Math., 140 (2004), 887--951 pdf.

8. Special cycles and derivatives of Eisenstein series, in Heegner points and Rankin L-series, Math. Sci. Res. Inst. Publ., 49,
243--270, Cambridge Univ. Press, Cambridge, 2004. pdf.
This expository article is based on a lecture given at the conference on Special values of Rankin L-series at MSRI in December of 2001.

9. Derivatives of Eisenstein series and arithmetic geometry, Proceedings of the ICM 2002, Beijing, Vol II, pp.173--183,
Higher Education Press, Beijing, 2002. pdf.
Article for a lecture at the ICM, Beijing, August 2002.

10. On a conjecture of Jacquet, (joint with Michael Harris), in Contributions to Automorphic Forms, Geometry and Arithmetic, H. Hida, D. Ramakrishnan, and F. Shahidi, eds., Johns Hopkins Press, Baltimore 2004, pp. 355--371. pdf.
We give a complete proof of the conjecture of Jacquet on the central value of the triple product L-function, based on the method of our earlier Annals paper, the Kim-Shahidi estimate towards the Ramanujan conjecture, and results of T. Ikeda, D. Ramakrishnan, and C.-B. Zhu.

11. Integrals of Borcherds forms, Compositio Math. 137 (2003), 293--349. pdf.

12. Modular forms and arithmetic geometry, in Current Developments in Mathematics, 2002, 135--180, International Press, Boston, 2003. pdf.
This expository article is based on two lectures given at Harvard, November 2002.

13. On first occurrence in the local theta correspondence, ( joint with S. Rallis) (to appear in the Proceedings of the Rallis 60th birthday conference) pdf.