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Volumn 2, Issue , 2006, Pages 421-457

Equidistribution, L-functions and ergodic theory: On some problems of Yu. Linnik

Author keywords

Automorphic L functions; Equidistribution; Ergodic theory; Subconvexity

Indexed keywords

EQUIDISTRIBUTION; ERGODIC THEORY; ERGODICS; L-FUNCTIONS; LARGE SPHERES; MODULAR FORMS; SUBCONVEXITY;

EID: 84878058558     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper
Times cited : (94)

References (83)
  • 1
    • 84878045036 scopus 로고    scopus 로고
    • Central value of automorphic
    • Preprint
    • Baruch, E. M., Mao, Z., Central value of automorphic L-functions. Preprint, 2003.
    • (2003) L-functions
    • Baruch, E.M.1    Mao, Z.2
  • 2
    • 0033244833 scopus 로고    scopus 로고
    • Analytic continuation of representations and estimates of automorphic forms
    • Bernstein, J., Reznikov, A., Analytic continuation of representations and estimates of automorphic forms. Ann. of Math. (2) 150 (1) (1999), 329-352.
    • (1999) Ann. of Math. (2) , vol.150 , Issue.1 , pp. 329-352
    • Bernstein, J.1    Reznikov, A.2
  • 4
  • 5
    • 52949086766 scopus 로고    scopus 로고
    • Non-vanishing of class group L-functions at the central point
    • Blomer,V., Non-vanishing of class group L-functions at the central point. Ann. Inst. Fourier (Grenoble) 54 (4) (2004), 831-847.
    • (2004) Ann. Inst. Fourier (Grenoble) , vol.54 , Issue.4 , pp. 831-847
    • Blomer, V.1
  • 6
    • 13244291523 scopus 로고    scopus 로고
    • Shifted convolution sums and subconvexity bounds for automorphic L-functions
    • - Shifted convolution sums and subconvexity bounds for automorphic L-functions. Internat. Math. Res. Notices (2004), (73), 3905-3926.
    • (2004) Internat. Math. Res. Notices , Issue.73 , pp. 3905-3926
    • Blomer, V.1
  • 7
    • 84878048029 scopus 로고    scopus 로고
    • A Burgess-like subconvex bound for twisted L-functions
    • to appear
    • Blomer, V., Harcos,G., Michel, Ph., A Burgess-like subconvex bound for twisted L-functions. Forum Math. (2006), to appear.
    • (2006) Forum Math.
    • Blomer, V.1    Harcos, G.2    Michel, Ph.3
  • 10
    • 54649083980 scopus 로고    scopus 로고
    • English transl. J. Math. Sci. (New York) 89 (1) (1998), 915-932.
    • (1998) J. Math. Sci. (New York) , vol.89 , Issue.1 , pp. 915-932
  • 11
    • 0035625382 scopus 로고    scopus 로고
    • Hecke operators and equidistribution of Hecke points
    • Clozel, L.,Oh, H.,Ullmo, E.,Hecke operators and equidistribution of Hecke points. Invent. Math. 144 (2) (2001), 327-351.
    • (2001) Invent. Math. , vol.144 , Issue.2 , pp. 327-351
    • Clozel, L.1    Oh, H.2    Ullmo, E.3
  • 13
    • 33644522591 scopus 로고    scopus 로고
    • Équidistribution de mesures algébriques
    • - Équidistribution de mesures algébriques, Compositio Math. 141 (5) (2005), 1255-1309.
    • (2005) Compositio Math. , vol.141 , Issue.5 , pp. 1255-1309
    • Clozel, L.1    Ullmo, E.2
  • 14
    • 85009863156 scopus 로고    scopus 로고
    • On sums of three squares
    • Cogdell, J.W.,On sums of three squares. J. Théor. Nombres Bordeaux 15 (1) (2003), 33-44.
    • (2003) J. Théor. Nombres Bordeaux , vol.15 , Issue.1 , pp. 33-44
    • Cogdell, J.W.1
  • 15
    • 24144441028 scopus 로고    scopus 로고
    • Hyperbolic equidistribution problems on Siegel 3-folds and Hilbert modular varieties
    • Cohen, P. B., Hyperbolic equidistribution problems on Siegel 3-folds and Hilbert modular varieties. Duke Math. J. 129 (1) (2005), 87-127.
    • (2005) Duke Math. J. , vol.129 , Issue.1 , pp. 87-127
    • Cohen, P.B.1
  • 16
    • 0034347513 scopus 로고    scopus 로고
    • The cubic moment of central values of automorphic
    • Conrey, J. B., Iwaniec, H., The cubic moment of central values of automorphic L-functions. Ann. of Math. (2) 151 (3) (2000), 1175-1216.
    • (2000) L-functions. Ann. of Math. (2) , vol.151 , Issue.3 , pp. 1175-1216
    • Conrey, J.B.1    Iwaniec, H.2
  • 18
    • 34250086530 scopus 로고
    • Hyperbolic distribution problems and half-integral weight Maass forms
    • Duke,W., Hyperbolic distribution problems and half-integral weight Maass forms. Invent. Math. 92 (1) (1988), 73-90.
    • (1988) Invent. Math. , vol.92 , Issue.1 , pp. 73-90
    • Duke, W.1
  • 26
    • 84973998259 scopus 로고
    • Density of integer points on affine homogeneous varieties
    • Duke, W., Rudnick, Z., Sarnak, P., Density of integer points on affine homogeneous varieties, Duke Math. J. 71 (1) (1993), 143-179.
    • (1993) Duke Math. J. , vol.71 , Issue.1 , pp. 143-179
    • Duke, W.1    Rudnick, Z.2    Sarnak, P.3
  • 27
    • 0002358904 scopus 로고
    • Representation of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids
    • Duke,W., Schulze-Pillot, R., Representation of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids. Invent. Math. 99 (1) (1990), 49-57.
    • (1990) Invent. Math. , vol.99 , Issue.1 , pp. 49-57
    • Duke, W.1    Schulze-Pillot, R.2
  • 28
    • 33746057062 scopus 로고    scopus 로고
    • Invariant measures and the set of exceptions to Littlewoods conjecture
    • to appear
    • Einsiedler, M., Katok, A., Lindenstrauss, E., Invariant measures and the set of exceptions to Littlewoods conjecture. Ann. of. Math. (2006), to appear.
    • (2006) Ann. Of. Math.
    • Einsiedler, M.1    Katok, A.2    Lindenstrauss, E.3
  • 29
    • 37849037302 scopus 로고    scopus 로고
    • Diagonalizable flows on locally homogeneous spaces and number theory
    • (Madrid), EMS Publishing House, Zürich 2006
    • Einsiedler,M., Lindenstrauss, E.,Diagonalizable flows on locally homogeneous spaces and number theory. In Proceedings of the International Congress of Mathematicians (Madrid, 2006), Volume II, EMS Publishing House, Zürich 2006, 1731-1759.
    • (2006) Proceedings of the International Congress of Mathematicians , vol.2 , pp. 1731-1759
    • Einsiedler, M.1    Lindenstrauss, E.2
  • 32
    • 84973997991 scopus 로고
    • Mixing counting, and equidistribution in Lie groups
    • Eskin, A.,McMullen, C.,Mixing, counting, and equidistribution in Lie groups. Duke Math. J. 71 (1) (1993), 181-209.
    • (1993) Duke Math. J. , vol.71 , Issue.1 , pp. 181-209
    • Eskin, A.1    McMullen, C.2
  • 33
    • 0030535375 scopus 로고    scopus 로고
    • Unipotent flows and counting lattice points on homogeneous varieties
    • Eskin, A., Mozes, Sh., Shah, N., Unipotent flows and counting lattice points on homogeneous varieties. Ann. of Math. (2) 143 (2) (1996), 253-299.
    • (1996) Ann. of Math. (2) , vol.143 , Issue.2 , pp. 253-299
    • Eskin, A.1    Mozes, Sh.2    Shah, N.3
  • 34
    • 0001560709 scopus 로고    scopus 로고
    • Counting problems and semisimple groups
    • Proceedings of the International Congress of Mathematicians (Berlin), Extra Vol. ICM Berlin, 1998
    • Eskin, A., Counting problems and semisimple groups. In Proceedings of the International Congress of Mathematicians (Berlin, 1998), Vol. II, Doc. Math., J. DMV, Extra Vol. ICM Berlin, 1998, 539-552.
    • (1998) Doc. Math., J. DMV , vol.2 , pp. 539-552
    • Eskin, A.1
  • 36
    • 0345865434 scopus 로고    scopus 로고
    • Equidistribution of integer points on a family of homogeneous varieties: A problem of Linnik
    • Gan,W. T.,Oh, H., Equidistribution of integer points on a family of homogeneous varieties: a problem of Linnik. Compositio Math. 136 (3) (2003), 323-352.
    • (2003) Compositio Math. , vol.136 , Issue.3 , pp. 323-352
    • Gan, W.T.1    Oh, H.2
  • 37
    • 0000489214 scopus 로고
    • Heights and the special values of L-series
    • (Montreal, Que.), CMS Conf. Proc. 7, Amer. Math. Soc., Providence, RI
    • Gross, B., Heights and the special values of L-series. In Number theory (Montreal, Que., 1985), CMS Conf. Proc. 7, Amer. Math. Soc., Providence, RI, (1987, 115-187.
    • (1985) Number Theory , pp. 115-187
    • Gross, B.1
  • 38
    • 0000205228 scopus 로고
    • Heegner points and derivatives of L-series
    • Gross, B., Zagier, D., Heegner points and derivatives of L-series. Invent. Math. 84 (2) (1986), 225-320.
    • (1986) Invent. Math. , vol.84 , Issue.2 , pp. 225-320
    • Gross, B.1    Zagier, D.2
  • 39
    • 13244295961 scopus 로고    scopus 로고
    • An additive problem in the Fourier coefficients of cusp forms
    • Harcos, G.,An additive problem in the Fourier coefficients of cusp forms. Math. Ann. 326 (2) (2003), 347-365.
    • (2003) Math. Ann. , vol.326 , Issue.2 , pp. 347-365
    • Harcos, G.1
  • 40
    • 32144435274 scopus 로고    scopus 로고
    • The subconvexity problem for Rankin-Selberg L-functions and equidistribution of Heegner points II
    • Harcos, G., Michel, Ph., The subconvexity problem for Rankin-Selberg L-functions and equidistribution of Heegner points II. Invent. Math. 163 (3) (2006), 581-655.
    • (2006) Invent. Math. , vol.163 , Issue.3 , pp. 581-655
    • Harcos, G.1    Michel, Ph.2
  • 41
    • 0000817033 scopus 로고
    • The central critical value of a triple product
    • Harris, M., Kudla, S. S., The central critical value of a triple product L-function. Ann. of Math. (2) 133 (3) (1991) 605-672.
    • (1991) L-function. Ann. of Math. (2) , vol.133 , Issue.3 , pp. 605-672
    • Harris, M.1    Kudla, S.S.2
  • 42
    • 0000207773 scopus 로고
    • Fourier coefficients of modular forms of half-integral weight
    • Iwaniec, H., Fourier coefficients of modular forms of half-integral weight. Invent. Math. 87 (2) (1987), 385-401.
    • (1987) Invent. Math. , vol.87 , Issue.2 , pp. 385-401
    • Iwaniec, H.1
  • 43
    • 0000535914 scopus 로고
    • The spectral growth of automorphic L-functions
    • - The spectral growth of automorphic L-functions. J. Reine Angew. Math. 428 (1992), 139-159.
    • (1992) J. Reine Angew. Math. , vol.428 , pp. 139-159
    • Iwaniec, H.1
  • 44
    • 77953538379 scopus 로고    scopus 로고
    • Harmonic analysis in number theory
    • (Princeton, NJ), Amer. Math. Soc., Providence, RI
    • - Harmonic analysis in number theory. In Prospects in mathematics (Princeton, NJ, 1996), Amer. Math. Soc., Providence, RI, 1999, 51-68.
    • (1996) Prospects in Mathematics , pp. 51-68
    • Iwaniec, H.1
  • 45
    • 0000379173 scopus 로고    scopus 로고
    • Perspectives on the analytic theory of L-functions
    • Special Volume
    • Iwaniec, H., Sarnak, P., Perspectives on the analytic theory of L-functions. Geom. Funct. Anal. (2000) Special Volume, 705-741.
    • (2000) Geom. Funct. Anal. , pp. 705-741
    • Iwaniec, H.1    Sarnak, P.2
  • 46
    • 13244278547 scopus 로고    scopus 로고
    • Convolutions of Fourier coefficients of cusp forms
    • Jutila, M., Convolutions of Fourier coefficients of cusp forms. Publ. Inst. Math. (Beograd) (N.S.) 65 (79) (1999), 31-51.
    • (1999) Publ. Inst. Math. (Beograd) (N.S.) , vol.65 , Issue.79 , pp. 31-51
    • Jutila, M.1
  • 47
    • 33644525667 scopus 로고    scopus 로고
    • Uniform bounds for Hecke L-functions
    • Jutila, M., Motohashi,Y., Uniform bounds for Hecke L-functions. Acta Math. 195 (2005), 61-115.
    • (2005) Acta Math. , vol.195 , pp. 61-115
    • Jutila, M.1    Motohashi, Y.2
  • 48
    • 51249168552 scopus 로고
    • Heegner points, cycles and Maass forms
    • Katok, S., Sarnak, P., Heegner points, cycles and Maass forms. Israel J. Math. 84 (1-2) (1993), 193-227.
    • (1993) Israel J. Math. , vol.84 , Issue.1-2 , pp. 193-227
    • Katok, S.1    Sarnak, P.2
  • 49
    • 0037248070 scopus 로고    scopus 로고
    • Functoriality for the exterior square of GL4 and the symmetric fourth of GL2
    • Kim, H., Functoriality for the exterior square of GL4 and the symmetric fourth of GL2. J. Amer. Math. Soc. 16 (1) (2003), 139-183.
    • (2003) J. Amer. Math. Soc. , vol.16 , Issue.1 , pp. 139-183
    • Kim, H.1
  • 51
    • 0001677208 scopus 로고
    • Values of L-series of modular forms at the center of the critical strip
    • Kohnen, W., Zagier, D., Values of L-series of modular forms at the center of the critical strip. Invent. Math. 64 (2) (1981), 175-198.
    • (1981) Invent. Math. , vol.64 , Issue.2 , pp. 175-198
    • Kohnen, W.1    Zagier, D.2
  • 52
    • 0034348174 scopus 로고    scopus 로고
    • Mollification of the fourth moment of automorphic L-functions and arithmetic applications
    • Kowalski, E.,Michel, Ph.,VanderKam, J., Mollification of the fourth moment of automorphic L-functions and arithmetic applications. Invent. Math. 142 (1) (2000), 95-151.
    • (2000) Invent. Math. , vol.142 , Issue.1 , pp. 95-151
    • Kowalski, E.1    Michel, Ph.2    Vanderkam, J.3
  • 54
    • 33644586868 scopus 로고    scopus 로고
    • Invariant measures and arithmetic quantum unique ergodicity
    • Lindenstrauss, E., Invariant measures and arithmetic quantum unique ergodicity. Ann. of Math. (2) 163 (1) (2006), 165-219.
    • (2006) Ann. of Math. (2) , vol.163 , Issue.1 , pp. 165-219
    • Lindenstrauss, E.1
  • 55
    • 84878099669 scopus 로고
    • The asymptotic distribution of reduced binary quadratic forms in relation to the geometries of Lobačevskiǐ. III
    • Linnik, Yu. V., The asymptotic distribution of reduced binary quadratic forms in relation to the geometries of Lobačevskiǐ. III. Vestnik Leningrad. Univ. 10 (8) (1955), 15-27.
    • (1955) Vestnik Leningrad. Univ. , vol.10 , Issue.8 , pp. 15-27
    • Linnik, Yu.V.1
  • 56
    • 84878080670 scopus 로고
    • Asymptotic-geometric and ergodic properties of sets of lattice points on a sphere
    • - Asymptotic-geometric and ergodic properties of sets of lattice points on a sphere. Amer. Math. Soc. Transl. (2) 13 (1960), 9-27.
    • (1960) Amer. Math. Soc. Transl. (2) , vol.13 , pp. 9-27
    • Linnik, Yu.V.1
  • 57
    • 0002648586 scopus 로고
    • Additive problems and eigenvalues of the modular operators
    • (Stockholm), Inst. Mittag-Leffler, Djursholm
    • - Additive problems and eigenvalues of the modular operators. In Proceedings of the International Congress of Mathematicians (Stockholm, 1962), Inst. Mittag-Leffler, Djursholm 1963, 270-284.
    • (1962) Proceedings of the International Congress of Mathematicians , pp. 270-284
    • Linnik, Yu.V.1
  • 58
    • 0003478111 scopus 로고
    • Ergodic properties of algebraic fields
    • Springer-Verlag, NewYork
    • - Ergodic properties of algebraic fields. Ergeb. Math. Grenzgeb. 45, Springer-Verlag, NewYork 1968.
    • (1968) Ergeb. Math. Grenzgeb. , vol.45
    • Linnik, Yu.V.1
  • 60
    • 0040959287 scopus 로고    scopus 로고
    • Problems and conjectures in rigidity theory
    • Amer. Math. Soc., Providence, RI
    • Margulis, G., Problems and conjectures in rigidity theory. In Mathematics: frontiers and perspectives, Amer. Math. Soc., Providence, RI, 2000, 161-174.
    • (2000) Mathematics: Frontiers and Perspectives , pp. 161-174
    • Margulis, G.1
  • 61
    • 13244251593 scopus 로고    scopus 로고
    • The subconvexity problem for Rankin-Selberg L-functions and equidistribution of Heegner points
    • Michel, Ph., The subconvexity problem for Rankin-Selberg L-functions and equidistribution of Heegner points. Ann. of Math. (2), 160 (1) (2004), 185-236.
    • (2004) Ann. of Math. (2) , vol.160 , Issue.1 , pp. 185-236
    • Michel, Ph.1
  • 64
    • 0037082233 scopus 로고    scopus 로고
    • Upper and lower bounds at s = 1 for certain Dirichlet series with Euler product
    • Molteni, G., Upper and lower bounds at s = 1 for certain Dirichlet series with Euler product. Duke Math. J. 111 (1) (2002), 133-158.
    • (2002) Duke Math. J. , vol.111 , Issue.1 , pp. 133-158
    • Molteni, G.1
  • 66
    • 4744350820 scopus 로고    scopus 로고
    • Hardy-Littlewood system and representations of integers by an invariant polynomial
    • Oh, Hee, Hardy-Littlewood system and representations of integers by an invariant polynomial. Geom. Funct. Anal. 14 (4) (2004), 791-809.
    • (2004) Geom. Funct. Anal. , vol.14 , Issue.4 , pp. 791-809
    • Oh, H.1
  • 67
    • 33845347365 scopus 로고    scopus 로고
    • Central values of Rankin L-series over real quadratic fields
    • to appear
    • Popa, A., Central values of Rankin L-series over real quadratic fields. Compositio Math. (2006), to appear.
    • (2006) Compositio Math.
    • Popa, A.1
  • 69
    • 0013136743 scopus 로고
    • Diophantine problems and linear groups
    • (Kyoto), The Mathematical Society of Japan, Tokyo, Springer-Verlag, Tokyo
    • Sarnak, P., Diophantine problems and linear groups. In Proceedings of the International Congress of Mathematicians (Kyoto, 1990), Vol. I, The Mathematical Society of Japan, Tokyo, Springer-Verlag, Tokyo, 1991, 459-471.
    • (1990) Proceedings of the International Congress of Mathematicians , vol.1 , pp. 459-471
    • Sarnak, P.1
  • 70
    • 84963011841 scopus 로고
    • Integrals of products of eigenfunctions
    • 1994
    • - Integrals of products of eigenfunctions. Internat. Math. Res. Notices 1994 (6) (1994), 251-260.
    • (1994) Internat. Math. Res. Notices , Issue.6 , pp. 251-260
    • Sarnak, P.1
  • 71
    • 0035921251 scopus 로고    scopus 로고
    • Estimates for Rankin-Selberg L-functions and quantum unique ergodicity
    • - Estimates for Rankin-Selberg L-functions and quantum unique ergodicity. J. Funct. Anal. 184 (2) (2001)n 419-453.
    • (2001) J. Funct. Anal. , vol.184 , Issue.2 , pp. 419-453
    • Sarnak, P.1
  • 72
    • 33749551798 scopus 로고
    • The asymptotic distribution of integers on a hyperboloid of one sheet and ergodic theorems
    • Skubenko, B. F., The asymptotic distribution of integers on a hyperboloid of one sheet and ergodic theorems. Izv. Akad. Nauk SSSR Ser. Mat. 26 (1962), 721-752.
    • (1962) Izv. Akad. Nauk SSSR Ser. Mat. , vol.26 , pp. 721-752
    • Skubenko, B.F.1
  • 73
    • 14844315393 scopus 로고    scopus 로고
    • Théorie ergodique et géométrie arithmétique
    • (Beijing), Higher Ed. Press, Beijing 2002
    • Ullmo, E.,Théorie ergodique et géométrie arithmétique, In Proceedings of the International Congress of Mathematicians (Beijing, 2002), Vol. II, Higher Ed. Press, Beijing 2002, 197-206.
    • (2002) Proceedings of the International Congress of Mathematicians , vol.2 , pp. 197-206
    • Ullmo, E.1
  • 74
    • 0036005362 scopus 로고    scopus 로고
    • Uniform distribution of Heegner points
    • Vatsal, V., Uniform distribution of Heegner points. Invent. Math. 148 (1) (2002), 1-46.
    • (2002) Invent. Math. , vol.148 , Issue.1 , pp. 1-46
    • Vatsal, V.1
  • 75
    • 0037331479 scopus 로고    scopus 로고
    • Special values of anticyclotomic L-functions
    • - Special values of anticyclotomic L-functions. Duke Math. J. 116 (2) (2003), 219-261.
    • (2003) Duke Math. J. , vol.116 , Issue.2 , pp. 219-261
    • Vatsal, V.1
  • 77
    • 0000791311 scopus 로고
    • Sur les valeurs de certaines fonctions L automorphes en leur centre de symétrie
    • Waldspurger, J.-L., Sur les valeurs de certaines fonctions L automorphes en leur centre de symétrie. Compositio Math. 54 (2) (1985), 173-242.
    • (1985) Compositio Math. , vol.54 , Issue.2 , pp. 173-242
    • Waldspurger, J.-L.1
  • 78
    • 28444463471 scopus 로고    scopus 로고
    • Rankin triple products and quantum chaos
    • to appear
    • Watson, T., Rankin triple products and quantum chaos, Ann. of Math. (2006), to appear.
    • (2006) Ann. of Math.
    • Watson, T.1
  • 80
    • 33646509226 scopus 로고    scopus 로고
    • A conjecture of Yves André's
    • Yafaev, A., A conjecture of Yves André's. Duke Math. J. 132 (3) (2006), 393-407.
    • (2006) Duke Math. J. , vol.132 , Issue.3 , pp. 393-407
    • Yafaev, A.1
  • 81
    • 0035593314 scopus 로고    scopus 로고
    • Heights of Heegner points on Shimura curves
    • Zhang, S., Heights of Heegner points on Shimura curves. Ann. of Math. (2) 153 (1) (2001), 27-147.
    • (2001) Ann. of Math. (2) , vol.153 , Issue.1 , pp. 27-147
    • Zhang, S.1


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