On values of L-functions of totally real algebraic number fields at integers
Acta Arithmetica (1996)
- Volume: 76, Issue: 4, page 359-392
- ISSN: 0065-1036
Access Full Article
topHow to cite
topShigeaki Tsuyumine. "On values of L-functions of totally real algebraic number fields at integers." Acta Arithmetica 76.4 (1996): 359-392. <http://eudml.org/doc/206904>.
@article{ShigeakiTsuyumine1996,
author = {Shigeaki Tsuyumine},
journal = {Acta Arithmetica},
keywords = {special values of -functions; Eisenstein series; Hilbert modular forms; identities for divisor sums; relative class numbers; representation numbers},
language = {eng},
number = {4},
pages = {359-392},
title = {On values of L-functions of totally real algebraic number fields at integers},
url = {http://eudml.org/doc/206904},
volume = {76},
year = {1996},
}
TY - JOUR
AU - Shigeaki Tsuyumine
TI - On values of L-functions of totally real algebraic number fields at integers
JO - Acta Arithmetica
PY - 1996
VL - 76
IS - 4
SP - 359
EP - 392
LA - eng
KW - special values of -functions; Eisenstein series; Hilbert modular forms; identities for divisor sums; relative class numbers; representation numbers
UR - http://eudml.org/doc/206904
ER -
References
top- [1] A. G. van Asch, Modular forms of half-integral weight, some explicit arithmetic, Math. Ann. 262 (1983), 77-89. Zbl0508.10015
- [2] A. O. L. Atkin and J. Lehner, Hecke operator on Γ₀(m), Math. Ann. 185 (1970), 134-160.
- [3] P. Bachmann, Die Arithmetik von quadratischen Formen, part I, Leipzig, 1898.
- [4] P. T. Bateman, On the representations of a number as the sum of three squares, Trans. Amer. Math. Soc. 71 (1951), 70-101. Zbl0043.04603
- [5] H. Cohen, Variations sur un thème de Siegel et Hecke, Acta Arith. 30 (1976), 63-93. Zbl0291.10021
- [6] A. Costa, Modular forms and class number congruence, Acta Arith. 61 (1992), 101-118. Zbl0773.11066
- [7] P. Deligne and K. A. Ribet, Values of abelian L-functions at negative integers over totally real fields, Invent. Math. 59 (1980), 227-286. Zbl0434.12009
- [8] H. J. Godwin, Real quartic fields with small discriminant, J. London Math. Soc. 31 (1956), 478-485. Zbl0071.03401
- [9] H. G. Grundman, The arithmetic genus of Hilbert modular varieties over non-Galois cubic fields, J. Number Theory 37 (1991), 343-365. Zbl0715.11023
- [10] H. Hasse, Über die Klassenzahl abelscher Zahlkörper, Springer, Berlin, 1985.
- [11] E. Hecke, Theorie der Eisensteinschen Reihen höhere Stufe und ihre Anwendung auf Funktionentheorie und Arithmetik, Abh. Math. Sem. Univ. Hamburg 5 (1927), 199-224. Zbl53.0345.02
- [12] E. Hecke, Über die L-funktionen und den Dirichletschen Primzahlsatz für einen beliebigen Zahlkörper, Nachr. Gesell. Wiss. Göttingen 1917, 299-318. Zbl46.0256.03
- [13] H. Hida, On the values of Hecke's L-functions at nonpositive integers, J. Math. Soc. Japan 30 (1978), 249-278. Zbl0371.12014
- [14] H. Iwaniec, Fourier coefficients of modular forms of half-integral weight, Invent. Math. 87 (1987), 385-401. Zbl0606.10017
- [15] M. Newman, Bounds for class numbers, in: Proc. Sympos. Pure Math. 8, Amer. Math. Soc., 1965, 70-77.
- [16] R. Okazaki, On evaluation of L-functions over real quadratic fields, J. Math. Kyoto Univ. 31 (1994), 1125-1153. Zbl0776.11071
- [17] R. Schulze-Pillot, Thetareihen positiv definiter quadratischer Formen, Invent. Math. 75 (1984), 283-299. Zbl0533.10021
- [18] G. Shimura, The special values of the zeta functions associated with Hilbert modular forms, Duke Math. J. 45 (1978), 637-679. Zbl0394.10015
- [19] T. Shintani, On evaluation of zeta functions of totally real algebraic number fields at non-positive integers, J. Fac. Sci. Univ. Tokyo 23 (1976), 393-417. Zbl0349.12007
- [20] C. L. Siegel, Berechnung von Zetafunktionen an ganzzahligen Stellen, Nachr. Akad. Wiss. Göttingen, 1969, 87-102. Zbl0186.08804
- [21] S. Tsuyumine, Cusp forms for Γ₀(p) of weight 2, Bull. Fac. Ed. Mie Univ. 45 (1994), 7-25.
- [22] S. Tsuyumine, Evaluation of zeta functions of totally real algebraic number fields at non-positive integers, preprint. Zbl0899.11020
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.