Geodesic
On representations of numbers by sums of squares and quadratic fields
Archivum mathematicum, Tome 13 (1977) no. 1, pp. 29-40

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Classification : 11E16, 11P05, 11R11, 11R23 
Slavutsky, I. Sh. On representations of numbers by sums of squares and quadratic fields. Archivum mathematicum, Tome 13 (1977) no. 1, pp. 29-40. http://geodesic.mathdoc.fr/item/ARM_1977_13_1_a3/
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[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

[2] Batеman P.: On representations of number as the sums of three squares. Тrans. Amеr. Math. Soc., 71, N 1, 1951, 70-101. | MR

[3] Carlitz L.: Arithmetic properties of generalized Bernoulli numbers. Journ. für Math., 202,1959, 174-182. | MR | Zbl

[4] Cohеn H.: Sommes de carrès, fonctions L et forms modulaires. Comptе Rеnd. Acad. Sci. Paris, 277, N 17, 1973, 827-830.

[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

[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.

[7] Frеsnеl J.: Nombres de Bernoulli et fonctions L p-adiques. Ann. Inst. Fouriеr, N 17, 1967 (1968), 281-333. | MR

[8] Iwasawa K.: Lecture on p-adic L-functions. Ann. of Math. Studiеs, 1972, N74. | MR

[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.

[10] Kиcелёв A. A., Cлaвyтcкий И. Ш.: O нeкomopыx cpaвнeнuяx для кoлuчecmвa npeдcmaвлeнuй cyммaмu нeчëmнoгo чucлa квaдpamoв. ДAH CCCP, 143, 1962, 272-274.

[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.

[12] Kubota Т., Lеopoldt H. W.: Eine p-adische Theorie der Zetawerte I. Journ. füг Math., 214-215, 1964, 328-339. | MR

[13] Lеopoldt H. W.: Eine Verallgemeinerung der Bernoullischen Zahlen. Abhandl. Math. Sеminar Univ. Hamburg, 22, 1958, 131-140. | MR

[14] Лoмaдзе Г. A.: O npeдcmaвлeнuu чuceл cyммaмu квaдpamoв. Тþyды Тбилиccкoгo мaт. ин-тa, 16, 1948, 231-275.

[15] Лoмaдзе Г. A.: O npeдcmaвлeнuu чuceл cyммaмu нeчëmнoгo чucлa квaдpamoв. Тpyды Тбилиccкoгo мaт. ин-тa, 17, 1949, 281-314.

[16] Лoмaдзе Г. A.: K npeдcmaвлeнuю чuceл cyммaмu квaдpamoв. Тpyды Тбилиccкoгo мaт. ин-тa, 20, 1954, 47-87.

[17] Mordеll L. J.: A. Pellian equation's conjecture, 2. Journ. Lond. Math. Soc., 36,1961,282-288. | MR

[18] Narkiеwicz W.: Elementary and analytic theory of algebraic numbers. Warszawa, 1974.

[19] Шaфapевич И. P.: Дзema-фyнкцuя. Mocквa, MГУ, 1969.

[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.

[21] Slavutsky I. Sh.: On Mordell's theorem. Асtа Аrithm., II, N 1, 1965, 57-66. | MR

[22] Славутский И. Ш.: Л-функции локального поля и вещественное квадратичное поле. Известия ВУЗ'ов, Математика, № 2, 1969, 99-105. | MR | Zbl

[23] Славутский И. Ш.: Локальные свойства чисел Бернулли и обобщение теоремы Куммера-Вандивера. Известия ВУЗ'ов, Математика, № 3, 1972, 61-69. | MR | Zbl

[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.