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On Koyama's refinement of the prime geodesic theorem.

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Title: On Koyama's refinement of the prime geodesic theorem.
Authors: AVDISPAHIĆ, Muharem1
Source: Proceedings of the Japan Academy, Series A: Mathematical Sciences. Mar2018, Vol. 94 Issue 3, p21-24. 4p.
Subjects: Mathematics theorems, Integral theorems, Hyperbolic differential equations, Partial differential equations, Conservation laws (Mathematics)
Abstract: We give a new proof of the best presently-known error term in the prime geodesic theorem for compact hyperbolic surfaces, without the assumption of excluding a set of finite logarithmic measure. Stronger implications of the Gallagher-Koyama approach are derived, yielding to a further reduction of the error term outside a set of finite logarithmic measure. [ABSTRACT FROM AUTHOR]
Copyright of Proceedings of the Japan Academy, Series A: Mathematical Sciences is the property of Japan Academy and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
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  Data: We give a new proof of the best presently-known error term in the prime geodesic theorem for compact hyperbolic surfaces, without the assumption of excluding a set of finite logarithmic measure. Stronger implications of the Gallagher-Koyama approach are derived, yielding to a further reduction of the error term outside a set of finite logarithmic measure. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Proceedings of the Japan Academy, Series A: Mathematical Sciences is the property of Japan Academy and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.3792/pjaa.94.21
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      – Code: eng
        Text: English
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      – SubjectFull: Mathematics theorems
        Type: general
      – SubjectFull: Integral theorems
        Type: general
      – SubjectFull: Hyperbolic differential equations
        Type: general
      – SubjectFull: Partial differential equations
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      – SubjectFull: Conservation laws (Mathematics)
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      – TitleFull: On Koyama's refinement of the prime geodesic theorem.
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            – D: 01
              M: 03
              Text: Mar2018
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              Y: 2018
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