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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


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Volume 66, Issue 3

Issues

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:
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/ 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:
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/ Yoshio Tanigawa
Published Online: 2016-08-17 | DOI: https://doi.org/10.1515/ms-2015-0160

Abstract

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

References

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

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    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

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

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

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

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    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.

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[2]
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