ℚ-linear relations of special values of the Estermann zeta function

ArticleOriginal scientific text

Title

Authors ¹

Department of Liberal Arts, Kagoshima National College of Technology, 1460-1 Shinko, Hayato-cho, Aira-gun, Kagoshima 899-51, Japan

Estermann zeta function, ℚ-linear relation, Leopoldt's character coordinate

T. Estermann, On the representation of a number as the sum of two products, Proc. London Math. Soc. (2) 31 (1930), 123-133.
K. Girstmair, Character coordinates and annihilators of cyclotomic numbers, Manuscripta Math. 59 (1987), 375-389.
H. Hasse, Über die Klassenzahl Abelscher Zahlkörper, Akademie-Verlag, Berlin, 1952.
M. Ishibashi, The value of the Estermann zeta functions at s=0, Acta Arith. 73 (1995), 357-361.
K. Iwasawa, Lectures on p-adic L-functions, Ann. of Math. Stud. 74, Princeton Univ. Press, Princeton, N.J., 1972.
M. Jutila, On exponential sums involving the divisor function, J. Reine Angew. Math. 355 (1985), 173-190.
I. Kiuchi, On an exponential sum involving the arithmetic function $σ_{a} (n)$ , Math. J. Okayama Univ. 29 (1987), 93-105.
H. W. Leopoldt, Über die Hauptordnung der ganzen Elemente eines abelschen Zahlkörpers, J. Reine Angew. Math. 201 (1959), 119-149.
Y. Motohashi, Riemann-Siegel Formula, Lecture Notes, Univ. of Colorado, Boulder, 1987.