Abstract
In this paper we introduce a certain sum by using Dirichlet characters. We investigate the Riesz mean of the sum using the analytic properties of the MultipleL-function systematically.
Similar content being viewed by others
References
S. Akiyama andH. Ishikawa, On analytic continuation of multipleL-functions and related zetafunctions. Analytic Number Theory. C. Jia and K. Matsumoto, eds., 1–16, Dordrecht.
M. N. Huxley, Exponential sums and lattice points II. Proc. London Math. Soc. (3)66, no. 2, 279–301, (1993).
A. E. Ingham, The distribution of prime numbers. Cambridge.
H. Ishikawa, On analytic properties of a multipleL-function, Analytic Extension Formulas and their Applications. International society for Analysis, Applications and Computation Series, S. Saitoh, N. Hayashi and M. Yamamoto, eds., 105–122. Dordrecht.
A. Ivić, The Riemann Zeta-Function. New York 1985.
H. Iwaniec andC. J. Mozzochi, On the divisor and circle problems. J. Number Theory29, 60–93 (1988).
G. Kolesnik, On the order of ϕ(1/2+ti) and δ(R). Pacific J. Math.82, 107–122 (1982).
G. Kolesnik, On the method of exponent pairs. Acta Arith.45, 115–143 (1985).
H. E. Richert, Über Dirichletreihen mit Funktionalgleichung. Public. Inst. Math. (Belgrade)11, 73–124 (1957).
J. Suetsuna, Analytic number theory (Japanese), 2nd edition, 117–119 (1970).
G. Tenenbaum, Introduction to analytic and probabilistic number theory. Cambridge, 90–100 (1995).
Author information
Authors and Affiliations
Additional information
Eine überarbeitete Fassung ging am 6. 8. 2001 ein
Rights and permissions
About this article
Cite this article
Ishikawa, H. A multiple character sum and a multipleL-function. Arch. Math 79, 439–448 (2002). https://doi.org/10.1007/BF02638381
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02638381