Power moments of the error term in the approximate functional equation for ζ²(s)

• Autorzy: Aleksandar Ivić
• Języki publikacji: EN

Słowa kluczowe

EN

Riemann zeta-function; approximate functional equation; Voronoï formula for the divisor problem; d(n) the number of divisors of n

Kategorie tematyczne

• 11M06: ζ ( s ) and L ( s , χ )

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1993
• Tom: 65
• Numer: 2
• Strony: 137-145

Daty

wydano

1993

otrzymano

1992-12-02

Twórcy

autor

Aleksandar Ivić

• Katedra Matematike RGF-A, Universiteta u Beogradu, Djušina 7, 11000 Beograd, Serbia (Yugoslavia)

Bibliografia

• [1] D. R. Heath-Brown, The distribution and moments of the error term in the Dirichlet divisor problem, Acta Arith. 60 (1992), 389-415.
• [2] A. Ivić, Large values of the error term in the divisor problem, Invent. Math. 71 (1983), 513-520.
• [3] A. Ivić, The Riemann Zeta-function, Wiley, New York, 1985.
• [4] A. Ivić, Large values of certain number-theoretic error terms, Acta Arith. 56 (1990), 135-159.
• [5] H. Iwaniec and C. J. Mozzochi, On the divisor and circle problems, J. Number Theory 29 (1988), 60-93.
• [6] I. Kiuchi, An improvement on the mean value formula for the approximate functional equation of the square of the Riemann zeta-function, J. Number Theory, to appear.
• [7] I. Kiuchi, Power moments of the error term for the approximate functional equation of the Riemann zeta-function, Publ. Inst. Math. (Beograd) 52 (66) (1992), in print.
• [8] I. Kiuchi and K. Matsumoto, Mean value results for the approximate functional equation of the square of the Riemann zeta-function, Acta Arith. 61 (1992), 337-345.
• [9] T. Meurman, On the mean square of the Riemann zeta-function, Quart. J. Math. Oxford Ser. (2) 38 (1987), 337-343.
• [10] Y. Motohashi, A note on the approximate functional equation for ζ²(s), Proc. Japan Acad. Ser. A 59 (1983), 393-396 and II, Quart. J. Math. Oxford Ser. 469-472.
• [11] Y. Motohashi, Lectures on the Riemann-Siegel Formula, Ulam Seminar, Dept. Math., Colorado University, Boulder, 1987.
• [12] E. Preissmann, Sur la moyenne quadratique du terme de reste du problème du cercle, C. R. Acad. Sci. Paris 306 (1988), 151-154.
• [13] K.-C. Tong, On divisor problem III, Acta Math. Sinica 6 (1956), 515-541 (in Chinese).
• [14] K.-M. Tsang, Higher power moments of Δ(x), E(t) and P(x), Proc. London Math. Soc. (3) 65 (1992), 65-84.