Positivity of quadratic base change -functions
Bulletin de la Société Mathématique de France (2001)
- Volume: 129, Issue: 1, page 33-90
- ISSN: 0037-9484
Access Full Article
topAbstract
topHow to cite
topJacquet, Hervé, and Nan, Chen. "Positivity of quadratic base change $L$-functions." Bulletin de la Société Mathématique de France 129.1 (2001): 33-90. <http://eudml.org/doc/272403>.
@article{Jacquet2001,
abstract = {We show that certain quadratic base change $L$-functions for $\mathrm \{Gl\}(2)$ are non-negative at their center of symmetry.},
author = {Jacquet, Hervé, Nan, Chen},
journal = {Bulletin de la Société Mathématique de France},
keywords = {$L$-functions; positivity; quadratic base change},
language = {eng},
number = {1},
pages = {33-90},
publisher = {Société mathématique de France},
title = {Positivity of quadratic base change $L$-functions},
url = {http://eudml.org/doc/272403},
volume = {129},
year = {2001},
}
TY - JOUR
AU - Jacquet, Hervé
AU - Nan, Chen
TI - Positivity of quadratic base change $L$-functions
JO - Bulletin de la Société Mathématique de France
PY - 2001
PB - Société mathématique de France
VL - 129
IS - 1
SP - 33
EP - 90
AB - We show that certain quadratic base change $L$-functions for $\mathrm {Gl}(2)$ are non-negative at their center of symmetry.
LA - eng
KW - $L$-functions; positivity; quadratic base change
UR - http://eudml.org/doc/272403
ER -
References
top- [1] Asai ( T.) – On certain Dirichlet series associated with Hilbert modular forms, Math. Ann., t.226 (1977), pp.81–94. Zbl0326.10024MR429751
- [2] Arthur ( J.) – A trace formula for reductive groups I: Terms associated to classes in , Duke Math. J., t.45 (1978), 911-952. Zbl0499.10032MR518111
- [3] Bernstein ( J.) – P-invariant distributions of and the classification of unitary representations of (non Archimedean case), in Lie Group Representations II, College Park, Md., 1982/1983, Lecture Notes in Math. 1041, Springer-Verlag, 1984. Zbl0541.22009MR748505
- [4] Bump ( D.), Friedberg ( S.), Hoffstein ( J.) – Eisenstein series on the metaplectic group and non-vanishing theorems for automorphic -functions, Ann. of Math., t.131 (1990), pp.53–127. Zbl0699.10039MR1038358
- [5] Baruch ( E.M.), Mao ( Z.) – Central critical value of automorphic -functions, preprint Zbl1191.11012
- [6] Casselman ( W.), Hecht ( H.), Miličic ( D.) – Bruhat filtrations and Whittaker vectors for real groups, preprint. Zbl0959.22010
- [7] Dixmier ( J.), Malliavin ( P.) – Factorizations de fonctions et vecteurs indéfiniment différentiables, Bull. Soc. Math. France, t.102 (1978), pp.305–330. Zbl0392.43013MR517765
- [8] Flicker ( Y.) – Twisted tensors and Euler products, Bull. Soc. Math. France, t.116 (1988), pp.295–313. Zbl0674.10026MR984899
- [9] Flicker ( Y.) – On distinguished representations, J. reine angew Math., t.418 (1991), pp.139–172. Zbl0725.11026MR1111204
- [10] Flicker ( Y.) – A Fourier summation formula for the symmetric space , Comp. Math., t.88 (1992), pp.39–117. Zbl0789.11035MR1234976
- [11] Flicker ( Y.) – Orbital Integrals on symmetric spaces and spherical characters, J. Algebra, t.184 (1996), pp.705–754. Zbl0856.22022MR1409236
- [12] Flicker ( Y.), Zinoniev ( D.) – On the poles of twisted -functions, Proc. Japan Acad. Sci., t.71 (1995), pp.114–116. Zbl0983.11023MR1344660
- [13] Friedberg ( S.), Hoffstein ( J.) – Non vanishing theorem for automorphic -functions for , Ann. of Math., t.142 (1995), pp.385–423. Zbl0847.11026
- [14] Guo ( J.) – On the positivity of the central critical value of automorphic -functions for , Duke Math. J., t.83 (1996), pp.157–189. Zbl0861.11032MR1388847
- [15] Guo ( J.) – On a generalization of a result of Waldspurger, Canad. J. Math., t.48 (1996), pp.105–142. Zbl0852.11026MR1382478
- [16] Gross ( B.) – Heights and the special values of series, in Number Theory (Montreal, Que., 1985), 115–187, CMS Conf. Proc. 7, Americ. Math. Soc., Providence, RI, 1987. Zbl0623.10019MR894322
- [17] Gross ( B.), Zagier ( D.) – Heegner points and derivatives of automorphic -functions for , Invent. Math., t.84 (1986), pp.225–320. Zbl0608.14019MR833192
- [18] Hakim ( J.) – Distinguished -adic representations, Duke Math. J., t.62 (1991), pp.1–22. Zbl0724.22016MR1104321
- [19] Harder ( G.), Langlands ( R.P.), Rapoport ( M.) – Algebraische Zyklen auf Hilbert–Blumenthal-Flächen, J. reine angew. Math., t.366 (1986), pp.53–120. Zbl0575.14004MR833013
- [20] Jacquet ( H.) – Sur un résultat de Waldspurger, Ann. Scient. École Norm. Sup., t.19 (1986), pp.185–229. Zbl0605.10015MR868299
- [21] Jacquet ( H.) – Sur un résultat de Waldspurger II, Comp. Math., t.63 (1987), pp.315–389. Zbl0633.10029MR909385
- [22] Jacquet ( H.), Lai ( K.) – A relative trace formula, Comp. Math., t.54 (1995), pp.243–310. Zbl0587.12006MR783512
- [23] Jacquet ( H.), Lai ( K.), Rallis ( S.)A trace formula for symmetric spaces, Duke Math. J., t.70 (1993), pp.305–371. Zbl0795.22008MR1219816
- [24] Jacquet ( H.), Lapid ( E.), Rogawski ( J.) – Periods of automorphic forms, J. Amer. Math. Soc., t.12 (1999), pp.173–240. Zbl1012.11044MR1625060
- [25] Jacquet ( H.), Ye ( Y.) – Une remarque sur le changement de base quadratique, C. R. Acad. Sci. Paris Sér. I Math., t.311 (1990), pp.671–676. Zbl0715.11026MR1081622
- [26] Khonen ( W.) – Fourier coefficients of modular forms of half integral weight, Math. Ann., t.271 (1985), pp.237–268. Zbl0542.10018MR783554
- [27] Kamal Khuri-Makdsi – On the Fourier coefficients of non holomorphic Hilbert modular forms of half integral weight, Duke Math. J., t.84 (1996), pp.399–452. Zbl0859.11031MR1404335
- [28] Katok ( S.), Sarnak ( P.) – Heegner points, cycles, and Maass forms, Israel J. Math., t.84 (1993), pp.193–227. Zbl0787.11016MR1244668
- [29] Kohnen ( W.), Zagier ( D.) – Values of -series of modular forms at the center of the critical strip, Invent. Math., t.64 (1981), pp.175–198. Zbl0468.10015MR629468
- [30] Rohrlich ( D.) – Non vanishing of -functions for , Invent. Math., t.97 (1989), pp.381–403. Zbl0677.10020
- [31] Rader ( C.), Rallis ( S.) – Spherical characters on p-adic symmetric spaces, Amer. J. Math., t.118 (1996), pp.91–178. Zbl0861.22011MR1375304
- [32] Shimura ( S.) – On Fourier coefficients of Hilbert modular forms of half-integral weight, Duke Math. J., t.71 (1993), pp.501–557. Zbl0802.11017MR1233447
- [33] Waldspurger ( J.-L.) – Corespondances de Shimura, J. Math. Pures Appl., t.59 (1980), pp.1–132. Zbl0412.10019MR577010
- [34] Waldspurger ( J.-L.) – Sur les coefficients de Fourier des formes modulaires de poids demi-entier, J. Math. Pures Appl., t.60 (1981), pp.375–484. Zbl0431.10015MR646366
- [35] Waldspurger ( J.-L.) – Quelques propriétés arithmétiques de certaines formes automorphes sur , Comp. Math., t.54 (1985), pp.121–171. Zbl0567.10022MR783510
- [36] Waldspurger ( J.-L.) – Sur les valeurs de fonctions -automorphes en leur centre de symétrie, Comp. Math., t.54 (1985), pp.173–242. Zbl0567.10021MR783511
- [37] Waldspurger ( J.-L.) – Correspondances de Shimura et quaternions, Forum Math., t.3 (1991), pp.219–307. Zbl0724.11026MR1103429
- [38] Wallach ( N.) – Real Reductive Groups II, Pure and Applied Mathematics, Vol 132-II (1192), Academic Press. Zbl0785.22001
- [39] Yang ( T.) – Theta liftings and Hecke -functions, J. reine angew. Math., t.485 (1997), pp.25–53. Zbl0867.11037MR1442188
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.