Derivatives of Eisenstein series and generating functions for arithmetic cycles
Séminaire Bourbaki : volume 1999/2000, exposés 865-879, Astérisque, no. 276 (2002), Talk no. 876, 28 p.
@incollection{SB_1999-2000__42__341_0,
author = {Kudla, Stephen S.},
title = {Derivatives of {Eisenstein} series and generating functions for arithmetic cycles},
booktitle = {S\'eminaire Bourbaki : volume 1999/2000, expos\'es 865-879},
author = {Collectif},
series = {Ast\'erisque},
note = {talk:876},
publisher = {Soci\'et\'e math\'ematique de France},
number = {276},
year = {2002},
zbl = {1066.11026},
mrnumber = {1886765},
language = {en},
url = {http://archive.numdam.org/item/SB_1999-2000__42__341_0/}
}
TY  - CHAP
AU  - Kudla, Stephen S.
TI  - Derivatives of Eisenstein series and generating functions for arithmetic cycles
BT  - Séminaire Bourbaki : volume 1999/2000, exposés 865-879
AU  - Collectif
T3  - Astérisque
N1  - talk:876
PY  - 2002
DA  - 2002///
IS  - 276
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/SB_1999-2000__42__341_0/
UR  - https://zbmath.org/?q=an%3A1066.11026
UR  - https://www.ams.org/mathscinet-getitem?mr=1886765
LA  - en
ID  - SB_1999-2000__42__341_0
ER  - 
%0 Book Section
%A Kudla, Stephen S.
%T Derivatives of Eisenstein series and generating functions for arithmetic cycles
%B Séminaire Bourbaki : volume 1999/2000, exposés 865-879
%A Collectif
%S Astérisque
%Z talk:876
%D 2002
%N 276
%I Société mathématique de France
%G en
%F SB_1999-2000__42__341_0
Kudla, Stephen S. Derivatives of Eisenstein series and generating functions for arithmetic cycles, in Séminaire Bourbaki : volume 1999/2000, exposés 865-879, Astérisque, no. 276 (2002), Talk no. 876, 28 p. http://archive.numdam.org/item/SB_1999-2000__42__341_0/

[1] R. E. Borcherds, The Gross-Kohnen-Zagier Theorem in higher dimensions, Duke Math. J. 97 (1999), pp. 219-233. | MR | Zbl

[2] J.-F. Boutot and H. Carayol, Uniformisation $p$-adiques des courbes de Shimura, Astérisque 196-197 (1991), 45-158. | MR | Zbl

[3] P. Garrett, Decomposition of Eisenstein series: Rankin triple products, Annals of Math. 125 (1987), 209-235. | MR | Zbl

[4] H. Gillet and C. Soulé, Arithmetic intersection theory, Jour of IHES, 72 (1990), 94-174. | Numdam | MR | Zbl

[5] B. H. Gross, On canonical and quasi-canonical liftings, Inventiones Math. 84 (1986), 321-326. | MR | Zbl

[6] B. H. Gross and K. Keating, On the intersection of modular correspondences, Invent. Math. 112 (1993), 225-245. | MR | Zbl

[7] B. H. Gross and S. Kudla, Heights and the central critical values of triple product L-functions, Compositio Math., 81 (1992), 143-209. | Numdam | MR | Zbl

[8] B. H. Gross and D. Zagier, Heegner points and the derivatives of $L$-series, Inventiones math. 84 (1986), 225-320. | MR | Zbl

[9] M. Harris and S. Kudla, The central critical value of a triple product $L$-function, Annals of Math. 133 (1991), 605-672. | MR | Zbl

[10] S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, 1962. | MR | Zbl

[11] F. Hirzebruch and D. Zagier, Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus, Inventiones Math. 36 (1976), 57-113. | MR | Zbl

[12] Y. Kitaoka, A note on local densities of quadratic forms, Nagoya Math. J. 92 (1983), 145-152. | MR | Zbl

[13] S. Kudla, Algebraic cycles on Shimura varieties of orthogonal type, Duke Math. J. 86 (1997), 39-78. | MR | Zbl

[14] S. Kudla, Central derivatives of Eisenstein series and height pairings, Annals of Math. 146 (1997), 545-646. | MR | Zbl

[15] S. Kudla and J. Millson, The theta correspondence and harmonic forms I, Math. Annalen, 274 (1986), 353-378. | MR | Zbl

[16] S. Kudla and J. Millson, The theta correspondence and harmonic forms II, Math. Annalen, 277 (1987), 267-314. | MR | Zbl

[17] S. Kudla and J. Millson, Intersection numbers of cycles on locally symmetric spaces and Fourier coefficients of holomorphic modular forms in several complex variables, IHES 71 (1990), 121-172. | Numdam | MR | Zbl

[18] S. Kudla and S. Rallis, Degenerate principal series and invariant distributions, Israel J. Math., 69 (1990), 25-45 | MR | Zbl

[19] S. Kudla and S. Rallis, Ramified degenerate principal series representations for $Sp\left(n\right)$, Israel J. Math., 78 (1992), 209-256. | MR | Zbl

[20] S. Kudla and S. Rallis, A regularized Siegel-Weil formula: the first term identity, Annals of Math. 140 (1994), 1-80. | MR | Zbl

[21] S. Kudla and M. Rapoport, Cycles on Siegel $3$-folds and derivatives of Eisenstein series, Ann. École Norm. Sup. 33 (2000), 695-756. | Numdam | MR | Zbl

[22] S. Kudla and M. Rapoport, Arithmetic Hirzebruch-Zagier cycles, J. reine angew. Math. 515 (1999), 155-244. | MR | Zbl

[23] S. Kudla and M. Rapoport, Heights on Shimura curves and $p$-adic uniformization, Inventiones Math. (to appear)

[24] S. Kudla, M. Rapoport and T. Yang, On the derivative of an Eisenstein series of weight 1, Int. Math. Res. Notices No. 7 (1999), 347-385. | MR | Zbl

[25] S. Kudla, M. Rapoport and T. Yang (in preparation).

[26] B. Moonen, Models of Shimura varieties in mixed characteristics, in Galois Representations in Arithmetic Algebraic Geometry, A. J. Scholl and R. L. Taylor. eds., London Math. Society Lecture Note Series 254, Cambridge Univ. Press, 1998. | MR | Zbl

[27] I. I. Piatetski-Shapiro and S. Rallis, Rankin triple L-functions, Compositio Math. 64 (1987), 31-115. | Numdam | MR | Zbl

[28] I. Satake, Algebraic Structures of Symmetric Domains, Publ. of the Math. Soc. of Japan, 14, Iwanami Shoten and Princeton Univ. Press, 1980. | MR | Zbl

[29] F. Sato and Y. Hironaka, Local densities of representations of quadratic forms over p-adic integers (the non-dyadic case), J. Number Theory 83 (2000), 106- 136. | MR | Zbl

[30] G. Shimura, Confluent hypergeometric functions on tube domains, Math. Annalen 260 (1982), 269-302. | MR | Zbl

[31] H. Stamm, On the reduction of the Hilbert-Blumenthal-moduli scheme with ${\Gamma }_{0}\left(p\right)$-level structure, Forum Math. 9 (1997), 405-455. | Zbl

[32] C. Soulé, D. Abramovich, J.-F. Burnol, and J. Kramer, Lectures on Arakelov Geometry, Cambridge Stud. Adv. Math., vol 33, Cambridge U. Press, 1992. | MR | Zbl

[33] W. J. Sweet, The metaplectic case of the Weil-Siegel formula, thesis, Univ. of Maryland, 1990.

[34] T. Yang, An explicit formula for local densities of quadratic forms, J. Number Theory 72 (1998), 309-356. | MR | Zbl