Authors and affiliations
1 Department of Integrated Human Sciences (Mathematics), Hamamatsu University School of Medicine
Handayama 1-20-1, Higashi-ku, Hamamatsu city, Shizuoka, 431-3192, Japan
2 Department of Integrated Arts and Science, Okinawa National College of Technology
Nago, Okinawa, 905-2192, Japan
In this paper, we show the relation between the shifted sum of a number-theoretic error term and its continuous mean (integral). We shall obtain a certain expression of the shifted sum as a linear combination of the continuous mean with the Bernoulli polynomials as their coefficients. As an application of our theorem, we give better approximations of the continuous mean by a shifted sum.
- The circle problem
- Mean value of error terms
- Shifted sum
- Bernoulli polynomial
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Cite this paper
Furuya, J., & Tanigawa, Y. (2014). Mean values of the error term with shifted arguments in the circle problem. Notes on Number Theory and Discrete Mathematics, 20(2), 44-51.