The mean value theorem of an arithmetical error term in short intervals and its application
| Project/Area Number |
15K04778
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Nagoya University |
|---|
Principal Investigator |
Tanigawa Yoshio 名古屋大学, 多元数理科学研究科, 招へい教員 (50109261)
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
MINAMIDE Makoto 山口大学, 大学院創成科学研究科, 講師 (80596552)
|
|---|
| Project Period (FY) |
2015-04-01 – 2018-03-31
|
| Project Status |
Completed (Fiscal Year 2017)
|
| Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
|
|---|
| Keywords | 短区間平均値定理 / 数論的誤差項 / Tong型の公式 / 3 次元約数問題 / 符号変化 / shifted convolution / リーマンゼータ関数の導関数 / 近似関数等式 / Tong 型の公式 / ３次約数問題 / トング型の公式 / ヴォロノイ公式 / ゼータ関数の微分 / Tong型公式 / 数論的誤差項の符号変化 / shifted convolusion |
|---|
| Outline of Final Research Achievements |
We derived the mean square formula in short intervals for an arithmetical error term by using the Tong-type truncated formula which we had already established for zeta-functions in the extended Selberg class. We applied our theorems to the study of the three-dimensional divisor problems and got the new results for the shifted convolutions and the sign changes of its arithmetical error term. Furthermore,we remade our Tong-type truncated formula in term of the exponent of the mean square of the zeta-function on the critical line.
In 1999, Hall derived the approximate functional equations for the square of the derivative of the Reimann zeta-function and other functions. By generalizing the method of Titchmarsh, we improved the estimates of Hall's error terms.
|
Report
(4 results)
Research Products
(27 results)
-
-
-
-
[Journal Article] On a new circle problem2017
Author(s)
Jun Furuya, Makoto Minamide, Yoshio Tanigawa
-
Journal Title
Journal of the Australian Mathematical Society
Volume: 印刷中
Issue: 2
Pages: 231-249
DOI
Related Report
Peer Reviewed / Open Access / Acknowledgement Compliant
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
