On the Dedekind Zeta Function. II
| LEADER | caa a22 4500 | ||
|---|---|---|---|
| 001 | 605522545 | ||
| 003 | CHVBK | ||
| 005 | 20210128100745.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 210128e20150601xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s10958-015-2415-4 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10958-015-2415-4 | ||
| 100 | 1 | |a Fomenko |D O. |u St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia |4 aut | |
| 245 | 1 | 0 | |a On the Dedekind Zeta Function. II |h [Elektronische Daten] |c [O. Fomenko] |
| 520 | 3 | |a Let K n be a number field of degree n over ℚ. By A(x, K n ) denote the number of integral ideals of K n with norm ≤ x. For K 8 = ℚ − 1 m 4 $$ {K}_8=\mathbb{Q}\left(\sqrt{-1},\sqrt[4]{m}\right) $$ , K 8 = ℚ ε m 4 $$ {K}_8=\mathbb{Q}\left(\sqrt[4]{\varepsilon_m}\right) $$ , and K 16 = ℚ − 1 ε m 4 $$ {K}_{16}=\mathbb{Q}\left(\sqrt{-1},\sqrt[4]{\varepsilon_m}\right) $$ , where m is a positive square-free integer and ε m denotes the fundamental unit of ℚ m $$ \mathbb{Q}\left(\sqrt{m}\right) $$ , the author proves that A x K n = Λ n x + Δ x K n x K n , Δ x K n ≪ x 1 − 3 n + 2 + ε . $$ \begin{array}{cc}\hfill A\left(x,{K}_n\right)={\Lambda}_nx+\Delta \left(x,{K}_n\right)\left(x,{K}_n\right),\hfill & \hfill \Delta \left(x,{K}_n\right)\ll {x}^{1-\frac{3}{n+2}+\varepsilon }.\hfill \end{array} $$ This improves earlier results of E. Landau (1917) and W. G. Nowak (Math. Nachr., 161 (1993), 59-74) for the special cases indicated. Also the author treats Titchmarch's phenomenon for ζK n (s) and large values of Δ(x, K n ). Bibliography: 26 titles. | |
| 540 | |a Springer Science+Business Media New York, 2015 | ||
| 773 | 0 | |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 207/6(2015-06-01), 923-933 |x 1072-3374 |q 207:6<923 |1 2015 |2 207 |o 10958 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10958-015-2415-4 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10958-015-2415-4 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Fomenko |D O. |u St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 207/6(2015-06-01), 923-933 |x 1072-3374 |q 207:6<923 |1 2015 |2 207 |o 10958 | ||