| Presentation | 2022-10-26 A number that has an elementary trace function and no elementary sum approximation Keita Hiroshima, Akitoshi Kawamura, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | The sum approximation (from below) of an irrational number $alpha$ is the function that, given a nonnegative number $n$, outputs the index of the $n$th $1$ in the binary expansion of $alpha$. A trace function for $alpha$ is one that, given a rational number $q$, outputs a rational number that is closer to $alpha$ than $q$ is. We show that there exists an irrational number with an elementary trace function and without an elementary sum approximation. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Computable Analysis / Elementary functions / Representations for real numbers / Sum approximations / Trace functions |
| Paper # | COMP2022-19 |
| Date of Issue | 2022-10-19 (COMP) |
| Conference Information | |
| Committee | COMP |
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| Conference Date | 2022/10/26(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Kyusyu Univ. Nishijin Plaza |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | Theoretical Computer Science, etc |
| Chair | Hiroyuki Uno(Osaka Metropolitan Univ.) |
| Vice Chair | Shuji Kijima(Shiga Univ.) |
| Secretary | Shuji Kijima(Hosei Univ.) |
| Assistant | Ei Ando(Senshu Univ.) |
| Paper Information | |
| Registration To | Technical Committee on Theoretical Foundations of Computing |
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| Language | JPN-ONLY |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | A number that has an elementary trace function and no elementary sum approximation |
| Sub Title (in English) | |
| Keyword(1) | Computable Analysis |
| Keyword(2) | Elementary functions |
| Keyword(3) | Representations for real numbers |
| Keyword(4) | Sum approximations |
| Keyword(5) | Trace functions |
| 1st Author's Name | Keita Hiroshima |
| 1st Author's Affiliation | Kyoto University(Kyoto Univ.) |
| 2nd Author's Name | Akitoshi Kawamura |
| 2nd Author's Affiliation | Kyoto University(Kyoto Univ.) |
| Date | 2022-10-26 |
| Paper # | COMP2022-19 |
| Volume (vol) | vol.122 |
| Number (no) | COMP-229 |
| Page | pp.pp.30-31(COMP), |
| #Pages | 2 |
| Date of Issue | 2022-10-19 (COMP) |