메뉴 건너뛰기




Volumn 81, Issue 2, 1996, Pages 269-322

Zeros of principal L-functions and random matrix theory

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0000580673     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-96-08115-6     Document Type: Article
Times cited : (465)

References (35)
  • 1
    • 84974000762 scopus 로고
    • A nonvanishing result for twists of L-functions of GL(n)
    • L. BARTHEL AND D. RAMAKRISHNAN, A nonvanishing result for twists of L-functions of GL(n), Duke Math. J. 74 (1994), 681-700.
    • (1994) Duke Math. J. , vol.74 , pp. 681-700
    • Barthel, L.1    Ramakrishnan, D.2
  • 2
    • 0003231477 scopus 로고
    • Multiplicative number theory
    • 2nd ed., Springer-Verlag, New York
    • H. DAVENPORT, Multiplicative Number Theory, 2nd ed., Graduate Texts in Math. 74, Springer-Verlag, New York, 1980.
    • (1980) Graduate Texts in Math. , vol.74
    • Davenport, H.1
  • 3
    • 0242436583 scopus 로고
    • Statistical theory of the energy levels of complex systems, III
    • F. J. DYSON, Statistical theory of the energy levels of complex systems, III, J. Math. Phys. 3 (1962), 166-175.
    • (1962) J. Math. Phys. , vol.3 , pp. 166-175
    • Dyson, F.J.1
  • 4
    • 0002561264 scopus 로고
    • Representation of the group GL(n, K) where K is a local field
    • ed. by I. M. Gelfand, Wiley, New York
    • I. M. GELFAND AND D. KAZHDAN, "Representation of the group GL(n, K) where K is a local field" in Lie Groups and their Representations, ed. by I. M. Gelfand, Wiley, New York, 1974, 95-118.
    • (1974) Lie Groups and Their Representations , pp. 95-118
    • Gelfand, I.M.1    Kazhdan, D.2
  • 5
    • 0003285072 scopus 로고
    • Zeta functions of simple algebras
    • Springer-Verlag, Berlin
    • R. GODEMENT AND H. JACQUET, Zeta Functions of Simple Algebras, Lecture Notes in Math. 260, Springer-Verlag, Berlin, 1972.
    • (1972) Lecture Notes in Math. , vol.260
    • Godement, R.1    Jacquet, H.2
  • 6
    • 84963009292 scopus 로고
    • On the triple correlation of zeros of the zeta function
    • D. A. HEJHAL, On the triple correlation of zeros of the zeta function, Internat. Math. Res. Notices 1994, 293-302.
    • (1994) Internat. Math. Res. Notices , pp. 293-302
    • Hejhal, D.A.1
  • 7
    • 0002552638 scopus 로고
    • Principal L-functions of the linear group
    • Automorphic Forms, Representations, and L-Functions, part 2, American Math. Soc., Providence
    • H. JACQUET, "Principal L-Functions of the Linear Group" in Automorphic Forms, Representations, and L-Functions, part 2, Proc. Sympos. Pure Math. 33, American Math. Soc., Providence, 1979, 63-86.
    • (1979) Proc. Sympos. Pure Math. , vol.33 , pp. 63-86
    • Jacquet, H.1
  • 9
    • 0001032031 scopus 로고
    • Conducteur des représentations du groupe linéaire
    • _, Conducteur des représentations du groupe linéaire, Math. Ann. 256 (1981), 199-214.
    • (1981) Math. Ann. , vol.256 , pp. 199-214
  • 10
    • 0001201053 scopus 로고
    • On Euler products and the classification of automorphic representations I
    • H. JACQUET AND J. A. SHALIKA, On Euler products and the classification of automorphic representations I, Amer. J. Math. 103 (1981), 499-558.
    • (1981) Amer. J. Math. , vol.103 , pp. 499-558
    • Jacquet, H.1    Shalika, J.A.2
  • 11
    • 0000500648 scopus 로고
    • Rankin-Selberg convolutions: Archimedean theory
    • Festschrift in Honor of I. I. Piatetski-Shapiro on the Occasion of his Sixtieth Birthday, Weizmann, Jerusalem
    • _, "Rankin-Selberg convolutions: Archimedean theory" in Festschrift in Honor of I. I. Piatetski-Shapiro on the Occasion of his Sixtieth Birthday, Israel Math. Conf. Proc. 2, Weizmann, Jerusalem, 1990, 125-208.
    • (1990) Israel Math. Conf. Proc. , vol.2 , pp. 125-208
  • 12
    • 84972538834 scopus 로고
    • Toeplitz matrices, translation kernels, and a related problem in probability theory
    • M. KAC, Toeplitz matrices, translation kernels, and a related problem in probability theory, Duke Math. J. 21 (1954), 501-509.
    • (1954) Duke Math. J. , vol.21 , pp. 501-509
    • Kac, M.1
  • 14
    • 0002535841 scopus 로고
    • Problems in the theory of automorphic forms
    • Lectures in Modern Analysis and Applications, Springer-Verlag, New York
    • R. P. LANOLANDS, "Problems in the theory of automorphic forms" in Lectures in Modern Analysis and Applications, Lecture Notes in Math. 170, Springer-Verlag, New York, 1970, 18-86.
    • (1970) Lecture Notes in Math. , vol.170 , pp. 18-86
    • Lanolands, R.P.1
  • 16
  • 20
    • 0000308274 scopus 로고
    • The pair correlation of zeros of the zeta function
    • Analytic Number Theory, Amer. Math. Soc., Providence
    • H. L. MONTGOMERY, "The pair correlation of zeros of the zeta function" in Analytic Number Theory, Proc. Sympos. Pure Math. 24, Amer. Math. Soc., Providence, 1973, 181-193.
    • (1973) Proc. Sympos. Pure Math. , vol.24 , pp. 181-193
    • Montgomery, H.L.1
  • 21
    • 84968518845 scopus 로고
    • On the distribution of spacings between zeros of the zeta function
    • A. M. ODLYZKO, On the distribution of spacings between zeros of the zeta function, Math. Comp. 48 (1987), 273-308.
    • (1987) Math. Comp. , vol.48 , pp. 273-308
    • Odlyzko, A.M.1
  • 24
    • 0038856207 scopus 로고
    • Arithmetic dirichlet series: Conjectures
    • CIRM Merseille, to appear
    • _, Arithmetic Dirichlet series: conjectures, proceedings of conference in honor of G. Freiman, CIRM (Merseille, 1993), to appear.
    • (1993) Proceedings of Conference in Honor of G. Freiman
  • 25
    • 0002872653 scopus 로고
    • Über die anzahl der primzahlen unter einer gegebenen gröβe
    • B. RIEMANN, Über die Anzahl der Primzahlen unter einer gegebenen Gröβe, Montasb. der Berliner Akad. (1858/60) 671-680; in Gessamelte Mathematische Werke, 2nd ed., Teubner, Leipzig, 1982, # VII.
    • (1858) Montasb. der Berliner Akad. , pp. 671-680
    • Riemann, B.1
  • 26
    • 0040634413 scopus 로고
    • Teubner, Leipzig
    • B. RIEMANN, Über die Anzahl der Primzahlen unter einer gegebenen Gröβe, Montasb. der Berliner Akad. (1858/60) 671-680; in Gessamelte Mathematische Werke, 2nd ed., Teubner, Leipzig, 1982, # VII.
    • (1982) Gessamelte Mathematische Werke, 2nd Ed.
  • 27
    • 0002419697 scopus 로고
    • The n-level correlations of zeros of the zeta function
    • Z. RUDNICK AND P. SARNAK, The n-level correlations of zeros of the zeta function, C. R. Acad. Sci. Paris Sér. I Math. 319 (1994), 1027-1032.
    • (1994) C. R. Acad. Sci. Paris Sér. I Math. , vol.319 , pp. 1027-1032
    • Rudnick, Z.1    Sarnak, P.2
  • 28
    • 84966201811 scopus 로고
    • Numerical computations concerning the ERH
    • R. RUMELY, Numerical computations concerning the ERH, Math. Comp. 61 (1993), 415-440.
    • (1993) Math. Comp. , vol.61 , pp. 415-440
    • Rumely, R.1
  • 29
  • 30
    • 0003194178 scopus 로고
    • Old and new conjectures and results about a class of Dirichlet series
    • Springer-Verlag, Berlin
    • A. SELBERG, "Old and new conjectures and results about a class of Dirichlet series" in Collected Papers, Vol. 2, Springer-Verlag, Berlin, 1991, 47-65.
    • (1991) Collected Papers , vol.2 , pp. 47-65
    • Selberg, A.1
  • 32
    • 0040041094 scopus 로고    scopus 로고
    • Letter to J.-M. Deshouillers, 1981
    • _, Letter to J.-M. Deshouillers, 1981.
  • 33
    • 0000574754 scopus 로고
    • On certain L-functions
    • F. SHAHIDI, On certain L-functions, Amer. J. Math. 103 (1981), 297-355.
    • (1981) Amer. J. Math. , vol.103 , pp. 297-355
    • Shahidi, F.1
  • 34
    • 0000967894 scopus 로고
    • The multiplicity one theorem for GL(n)
    • J. SHALIKA, The multiplicity one theorem for GL(n), Ann. of Math. (2) 100 (1974), 171-193.
    • (1974) Ann. of Math. , vol.100 , Issue.2 , pp. 171-193
    • Shalika, J.1
  • 35
    • 84967710276 scopus 로고
    • A combinatorial lemma and its applications to probability theory
    • F. SPITZER, A combinatorial lemma and its applications to probability theory, Trans. Amer. Math. Soc. 82 (1956), 323-339.
    • (1956) Trans. Amer. Math. Soc. , vol.82 , pp. 323-339
    • Spitzer, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.