| Title:
|
On representations of numbers by sums of squares and quadratic fields (English) |
| Author:
|
Slavutsky, I. Sh. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
13 |
| Issue:
|
1 |
| Year:
|
1977 |
| Pages:
|
29-40 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11E16 |
| MSC:
|
11P05 |
| MSC:
|
11R11 |
| MSC:
|
11R23 |
| idZBL:
|
Zbl 0375.10031 |
| idMR:
|
MR0466049 |
| . |
| Date available:
|
2008-06-06T06:02:54Z |
| Last updated:
|
2012-05-09 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/106953 |
| . |
| Reference:
|
[1] Ankeny N. S., Artin E., Chowla S.: The class-numbers of real quadratic fields.Ann. of Math., 56, N 3, 1952, 479-493. MR 0049948 |
| Reference:
|
[2] Batеman P.: On representations of number as the sums of three squares.Тrans. Amеr. Math. Soc., 71, N 1, 1951, 70-101. MR 0042438 |
| Reference:
|
[3] Carlitz L.: Arithmetic properties of generalized Bernoulli numbers.Journ. für Math., 202,1959, 174-182. Zbl 0125.02202, MR 0109132 |
| Reference:
|
[4] Cohеn H.: Sommes de carrès, fonctions L et forms modulaires.Comptе Rеnd. Acad. Sci. Paris, 277, N 17, 1973, 827-830. |
| Reference:
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[5] Hardy G. H.: On the representation of a number as the sum of any number of squares, and in particular of five.Тrans. Amеr. Math. Soc., 21, 1920, 255-284. MR 1501144 |
| Reference:
|
[б] Hardy G. H.: On the representation of a number as the sum of any number of squares, and in particular of five and seven.Proc. Nat. Acad. Sci. USA, 4, 1918, 189-193. |
| Reference:
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[7] Frеsnеl J.: Nombres de Bernoulli et fonctions L p-adiques.Ann. Inst. Fouriеr, N 17, 1967 (1968), 281-333. MR 0224570 |
| Reference:
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[8] Iwasawa K.: Lecture on p-adic L-functions.Ann. of Math. Studiеs, 1972, N74. MR 0360526 |
| Reference:
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[9] Киcелёв A. A.: O нeкomopыx cpaвнeнuяx для чucлa клaccoв uдeaлoв вeщecmвeнныx квaдpamuчныx noлeй.Уч. зaп. ЛГУ, cеpия мaт. нayк, вып. 16, 1949, 20-31. |
| Reference:
|
[10] Kиcелёв A. A., Cлaвyтcкий И. Ш.: O нeкomopыx cpaвнeнuяx для кoлuчecmвa npeдcmaвлeнuй cyммaмu нeчëmнoгo чucлa квaдpamoв.ДAH CCCP, 143, 1962, 272-274. |
| Reference:
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[11] Kиcелёв A. A., Cлaвyтcкий И. Ш.: Пpeoбpaзoвaнue фopмyл Дupuxлe u apuфмemuчecкoe вычucлeнue чucлa клaccoв uдeaлoв квaдpamuчныx noлeй.Тpyды 4-гo Bcеcoюзн. мaт. cъездa, т. 2, Ленингpaд, 1964, 105-112. |
| Reference:
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[12] Kubota Т., Lеopoldt H. W.: Eine p-adische Theorie der Zetawerte I.Journ. füг Math., 214-215, 1964, 328-339. MR 0163900 |
| Reference:
|
[13] Lеopoldt H. W.: Eine Verallgemeinerung der Bernoullischen Zahlen.Abhandl. Math. Sеminar Univ. Hamburg, 22, 1958, 131-140. MR 0092812 |
| Reference:
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[14] Лoмaдзе Г. A.: O npeдcmaвлeнuu чuceл cyммaмu квaдpamoв.Тþyды Тбилиccкoгo мaт. ин-тa, 16, 1948, 231-275. |
| Reference:
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[15] Лoмaдзе Г. A.: O npeдcmaвлeнuu чuceл cyммaмu нeчëmнoгo чucлa квaдpamoв.Тpyды Тбилиccкoгo мaт. ин-тa, 17, 1949, 281-314. |
| Reference:
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[16] Лoмaдзе Г. A.: K npeдcmaвлeнuю чuceл cyммaмu квaдpamoв.Тpyды Тбилиccкoгo мaт. ин-тa, 20, 1954, 47-87. |
| Reference:
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[17] Mordеll L. J.: A. Pellian equation's conjecture, 2.Journ. Lond. Math. Soc., 36,1961,282-288. MR 0126411 |
| Reference:
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[18] Narkiеwicz W.: Elementary and analytic theory of algebraic numbers.Warszawa, 1974. |
| Reference:
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[19] Шaфapевич И. P.: Дзema-фyнкцuя.Mocквa, MГУ, 1969. |
| Reference:
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[20] Cлaвyтcкий И. Ш.: O чucлe клaccoв uдeaлoв вeщecmвeннoгo квaдpamuчнoгo noля c npocmым дucкpuмuнaнmoм.Уч. зaп. ЛЕHИHГPАДCKOГO Педaгoгичеcкoгo ин-тa им. Геpценa, 218, 1961, 179-189. |
| Reference:
|
[21] Slavutsky I. Sh.: On Mordell's theorem.Асtа Аrithm., II, N 1, 1965, 57-66. MR 0175883 |
| Reference:
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[22] Славутский И. Ш.: Л-функции локального поля и вещественное квадратичное поле.Известия ВУЗ'ов, Математика, № 2, 1969, 99-105. Zbl 1149.62317, MR 0251009 |
| Reference:
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[23] Славутский И. Ш.: Локальные свойства чисел Бернулли и обобщение теоремы Куммера-Вандивера.Известия ВУЗ'ов, Математика, № 3, 1972, 61-69. Zbl 1170.01322, MR 0303936 |
| Reference:
|
[24] Suetuna Z.: Über di Maximalordnung einiger Funktionen in der Idealtheorie.Journ. Sci. Univ. Тоkio, sect.I, 1, раrt 6, 1926, 249-283, ibid. раrt 9, 1927, 349-370. |
| . |
