Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

IMPACT FACTOR 2018: 0.490

CiteScore 2018: 0.47

SCImago Journal Rank (SJR) 2018: 0.279
Source Normalized Impact per Paper (SNIP) 2018: 0.627

Mathematical Citation Quotient (MCQ) 2018: 0.29

Print + Online
See all formats and pricing
More options …
Volume 66, Issue 3


Representations and evaluations of the error term in a certain divisor problem

Jun Furuya
  • Department of Integrated Arts and Science Okinawa National College of Technology Nago, Okinawa, 905-2192 JAPAN, Current address: Department of Integrated Human Sciences (Mathematics) Hamamatsu University School of Medicine Handayama 1-20-1, Hamamatsu, Shizuoka, 431-3192 JAPAN, E-mail:
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Makoto Minamide
  • Faculty of Science Kyoto Sangyo University Kamigamo, Kita-ku, Kyoto, 603-8555 JAPAN, Current address: Faculty of Science Yamaguchi University Yoshida 1677-1, Yamaguchi 753-8512 JAPAN, E-mail:
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Yoshio Tanigawa
Published Online: 2016-08-17 | DOI: https://doi.org/10.1515/ms-2015-0160


In this paper, we shall derive representations of the Chowla-Walum type formula for the error term in a divisor problem related to the derivatives of the Riemann zeta-function. As a direct corollary of this formula, we shall consider estimations of this error term.

MSC 2010: Primary 11N37, 11L07

Key words: Chowla-Walum formula; exponent pairs; hyperbola method


  • [1]

    Apostol, T. M.: Introduction to Analytic Number Theory. Undergrad. Texts Math., Springer-Verlag, New York-Heidelberg, 1976.Google Scholar

  • [2]

    Graham, S. W.—KOLESNIK, G.: Van der Corput's Method for Exponential Sums. London Math. Soc. Lecture Note Ser. 126, Cambridge University Press, Cambridge, 1991.Google Scholar

  • [3]

    Ivić, A.: The Riemann Zeta-Function, Theory and Applications, Dover Publications, Inc., Mineola, NY, 2003 (Reprint of the 1985 original (Wiely)).Google Scholar

  • [4]

    Krätzel, E.: Lattice Points, Kluwer Acad. Publishers, Dordrecht, 1988.Google Scholar

  • [5]

    Minamide, M.: The truncated Voronoï formula for the derivative of the Riemann zeta function, Indian J. Math. 55 (2013), 325–352.Google Scholar

  • [6]

    Montgomery, H. L.: Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis. CBMS Reg. Conf. Ser. Math. 84, Amer. Math. Soc., Washington, 1994.Google Scholar

About the article

Received: 2013-09-06

Accepted: 2013-12-05

Published Online: 2016-08-17

Published in Print: 2016-06-01

Citation Information: Mathematica Slovaca, Volume 66, Issue 3, Pages 575–582, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2015-0160.

Export Citation

© 2016 Mathematical Institute Slovak Academy of Sciences.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Jun Furuya, T. Makoto Minamide, and Yoshio Tanigawa
Canadian Journal of Mathematics, 2019, Page 1
Journal of the Australian Mathematical Society, 2016, Page 1
Debika Banerjee and Makoto Minamide
Journal of Mathematical Analysis and Applications, 2016, Volume 438, Number 2, Page 533

Comments (0)

Please log in or register to comment.
Log in