메뉴 건너뛰기




Volumn 85, Issue 2, 2000, Pages 263-282

Explicit Bounds for Residues of Dedekind Zeta Functions, Values of L-Functions at s=1, and Relative Class Numbers

Author keywords

Dedekind zeta functions; L functions; relative class number, CM field

Indexed keywords


EID: 0034368620     PISSN: 0022314X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jnth.2000.2545     Document Type: Article
Times cited : (56)

References (33)
  • 1
    • 0040302201 scopus 로고
    • On the zeta functions of algebraic number fields, II
    • Brauer R. On the zeta functions of algebraic number fields, II. Amer. J. Math. 72:1950;739-746.
    • (1950) Amer. J. Math. , vol.72 , pp. 739-746
    • Brauer, R.1
  • 2
    • 0030222811 scopus 로고    scopus 로고
    • The number of elliptic curves over Q with conductor N
    • Brumer A., Silverman J. H. The number of elliptic curves over Q with conductor N. Manuscripta Math. 91:1996;95-102.
    • (1996) Manuscripta Math. , vol.91 , pp. 95-102
    • Brumer, A.1    Silverman, J.H.2
  • 3
    • 84968515117 scopus 로고
    • On the computation of the class number of an algebraic number field
    • Buchmann J., Williams H. C. On the computation of the class number of an algebraic number field. Math. Comp. 53:1989;679-688.
    • (1989) Math. Comp. , vol.53 , pp. 679-688
    • Buchmann, J.1    Williams, H.C.2
  • 4
    • 0003647258 scopus 로고
    • Multiplicative Number Theory
    • W. J. Leveque. Chicago: Markham
    • Davenport H. Leveque W. J., Multiplicative Number Theory. Lectures in Advanced Mathematics. 1967;Markham, Chicago.
    • (1967) Lectures in Advanced Mathematics
    • Davenport, H.1
  • 5
    • 0002372931 scopus 로고
    • On Burgess' bound for primitive roots modulo primes and an application to Γ(p)
    • Grosswald E. On Burgess' bound for primitive roots modulo primes and an application to Γ(p). Amer. J. Math. 103:1981;1171-1183.
    • (1981) Amer. J. Math. , vol.103 , pp. 1171-1183
    • Grosswald, E.1
  • 6
    • 0004133524 scopus 로고
    • Section 12.14, The least solution to Pell's equation, Theorem 13.3. Berlin/New York: Springer-Verlag
    • Hua L. K. Introduction to Number Theory. Section 12.14, The least solution to Pell's equation, Theorem 13.3. 1982;Springer-Verlag, Berlin/New York.
    • (1982) Introduction to Number Theory
    • Hua, L.K.1
  • 8
    • 0002309077 scopus 로고
    • Zur Theorie der Heckeschen Zetafunktionen, welche komplexen Charakteren entsprechen
    • Landau E. Zur Theorie der Heckeschen Zetafunktionen, welche komplexen Charakteren entsprechen. Math. Z. 4:1919;152-162.
    • (1919) Math. Z. , vol.4 , pp. 152-162
    • Landau, E.1
  • 11
    • 0004259352 scopus 로고
    • Graduate Texts in Mathematics. New York/Berlin: Springer-Verlag
    • Lang S. Algebraic Number Theory. Graduate Texts in Mathematics. 110:1994;Springer-Verlag, New York/Berlin.
    • (1994) Algebraic Number Theory , vol.110
    • Lang, S.1
  • 12
    • 0002088414 scopus 로고
    • The product of the number of divisor classes by the regulator of an algebraic number field
    • Lavrik A. F., Edgorov Z. The product of the number of divisor classes by the regulator of an algebraic number field. Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat., Nauk. 2:1975;77-79.
    • (1975) Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat., Nauk , vol.2 , pp. 77-79
    • Lavrik, A.F.1    Edgorov, Z.2
  • 13
    • 84967712824 scopus 로고
    • Algorithms in algebraic number theory
    • Lenstra H. W. Algorithms in algebraic number theory. Bull. Amer. Math. Soc. 26:1992;211-244.
    • (1992) Bull. Amer. Math. Soc. , vol.26 , pp. 211-244
    • Lenstra, H.W.1
  • 14
    • 84941919624 scopus 로고
    • On the class number of the corpus P( -k )
    • Littlewood J. E. On the class number of the corpus P( -k ). Proc. London Math. Soc. 27:1928;358-372.
    • (1928) Proc. London Math. Soc. , vol.27 , pp. 358-372
    • Littlewood, J.E.1
  • 15
    • 0002838623 scopus 로고
    • Majorations explicites de |L(1, χ)|
    • Louboutin S. Majorations explicites de |L(1, χ)| C. R. Acad. Sci. Paris. 316:1993;11-14.
    • (1993) C. R. Acad. Sci. Paris , vol.316 , pp. 11-14
    • Louboutin, S.1
  • 16
    • 0001066431 scopus 로고    scopus 로고
    • Majorations explicites de |L(1, χ)| (Suite)
    • Louboutin S. Majorations explicites de |L(1, χ)| (suite). C. R. Acad. Sci. Paris. 323:1996;443-446.
    • (1996) C. R. Acad. Sci. Paris , vol.323 , pp. 443-446
    • Louboutin, S.1
  • 17
    • 0030294734 scopus 로고    scopus 로고
    • A finiteness theorem for imaginary abelian number fields
    • Louboutin S. A finiteness theorem for imaginary abelian number fields. Manuscripta Math. 91:1996;343-352.
    • (1996) Manuscripta Math. , vol.91 , pp. 343-352
    • Louboutin, S.1
  • 18
    • 0002734511 scopus 로고    scopus 로고
    • Majorations explicites du résidu au point 1 des fonctions zêta de certains corps de nombres
    • Louboutin S. Majorations explicites du résidu au point 1 des fonctions zêta de certains corps de nombres. J. Math. Soc. Japan. 50:1998;57-69.
    • (1998) J. Math. Soc. Japan , vol.50 , pp. 57-69
    • Louboutin, S.1
  • 19
    • 0032375202 scopus 로고    scopus 로고
    • Upper bounds on |L(1, χ)| and applications
    • Louboutin S. Upper bounds on |L(1, χ)| and applications. Canad. J. Math. 50:1998;794-815.
    • (1998) Canad. J. Math. , vol.50 , pp. 794-815
    • Louboutin, S.1
  • 20
    • 0000147448 scopus 로고
    • Abriss einer einheitlichen der Gamma und hypergeometrischen Funktionen
    • Mellin H. Abriss einer einheitlichen der Gamma und hypergeometrischen Funktionen. Math. Ann. 68:1910;305-337.
    • (1910) Math. Ann. , vol.68 , pp. 305-337
    • Mellin, H.1
  • 22
    • 0001232239 scopus 로고
    • Character sums and explicit estimates for L-functions
    • Peral Alonso J. C. Character sums and explicit estimates for L-functions. Contemp. Math. 189:1995;449-459.
    • (1995) Contemp. Math. , vol.189 , pp. 449-459
    • Peral Alonso, J.C.1
  • 23
    • 0002141770 scopus 로고
    • Elementary methods in the theory of L-functions. VII. Upper bound for L(1, χ)
    • Pintz J. Elementary methods in the theory of L-functions. VII. Upper bound for L(1, χ). Acta Arith. 32:1977;397-406.
    • (1977) Acta Arith. , vol.32 , pp. 397-406
    • Pintz, J.1
  • 24
    • 0002513603 scopus 로고
    • Une relation d'inégalité entre discriminant, nombre de classes et régulateur des corps de nombres
    • Quême R. Une relation d'inégalité entre discriminant, nombre de classes et régulateur des corps de nombres. C. R. Acad. Sci. Paris. 306:1988;5-10.
    • (1988) C. R. Acad. Sci. Paris , vol.306 , pp. 5-10
    • Quême, R.1
  • 25
    • 85037799369 scopus 로고
    • Relations d'inégalité effectives en théorie algébrique des nombres
    • Quême R. Relations d'inégalité effectives en théorie algébrique des nombres. Sém. Théor. Nombres, Univ. Bordeaux I. 1987/1988.
    • (1987) Sém. Théor. Nombres, Univ. Bordeaux I
    • Quême, R.1
  • 29
    • 0000314631 scopus 로고
    • Quick lower bounds for regulators of number fields
    • Skoruppa N.-P. Quick lower bounds for regulators of number fields. Enseign. Math. II. 39:1993;137-141.
    • (1993) Enseign. Math. II , vol.39 , pp. 137-141
    • Skoruppa, N.-P.1
  • 30
    • 0001468947 scopus 로고
    • Some effective cases of the Brauer-Siegel theorem
    • Stark H. M. Some effective cases of the Brauer-Siegel theorem. Invent. Math. 23:1974;135-152.
    • (1974) Invent. Math. , vol.23 , pp. 135-152
    • Stark, H.M.1
  • 31
    • 0002372089 scopus 로고
    • A property of L-functions on the real line
    • Stark H. M., Zagier D. A property of L-functions on the real line. J. Number Theory. 12:1980;49-52.
    • (1980) J. Number Theory , vol.12 , pp. 49-52
    • Stark, H.M.1    Zagier, D.2
  • 32
    • 0004116512 scopus 로고    scopus 로고
    • Graduate Texts in Mathematics. New York/Berlin: Springer-Verlag
    • Washington L. C. Introduction to Cyclotomic Fields. Graduate Texts in Mathematics. 83:1997;Springer-Verlag, New York/Berlin.
    • (1997) Introduction to Cyclotomic Fields , vol.83
    • Washington, L.C.1
  • 33
    • 0001450627 scopus 로고
    • Ideale kleiner Norm in Idealklassen und eine Regulatorabschätzung
    • Zimmert R. Ideale kleiner Norm in Idealklassen und eine Regulatorabschätzung. Invent. Math. 62:1981;367-380.
    • (1981) Invent. Math. , vol.62 , pp. 367-380
    • Zimmert, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.