Geodesic
A new application of $p$-adic analysis to representation of numbers by
Izvestiya. Mathematics , Tome 4 (1970) no. 5, pp. 1043-1069.

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An effective method is given for constructing bounds for unknowns in representations of numbers by binary forms. The arguments are based on bounds of linear forms in the logarithms of algebraic numbers in various metrics (archimedian and non-archimedian). 
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V. G. Sprindzhuk. A new application of $p$-adic analysis to representation of numbers by. Izvestiya. Mathematics , Tome 4 (1970) no. 5, pp. 1043-1069. http://geodesic.mathdoc.fr/item/IM2_1970_4_5_a4/

[1] Borevich Z. I., Shafarevich I. R., Teoriya chisel, Nauka, M., 1964 | MR

[2] Vinogradov A. I., Sprindzhuk V. G., “O predstavlenii chisel binarnymi formami”, Matem. zametki, 3:4 (1968), 369–376 | MR | Zbl

[3] Kassels Dzh. V. S., Vvedenie v teoriyu diofantovykh priblizhenii, M., 1961 | Zbl

[4] Leng S., Algebraicheskie chisla, Mir, M., 1966 | MR

[5] Lenskoi D. N., Funktsii v nearkhimedovski normirovannykh polyakh, Saratovsk. un-t, 1962 | MR | Zbl

[6] Sprindzhuk V. G., “K teoreme Beikera o lineinykh formakh s logarifmami”, Dokl. AN BSSR, 11:9 (1967), 767–769 | Zbl

[7] Sprindzhuk V. G., “Effektivizatsiya v nekotorykh zadachakh teorii diofantovykh priblizhenii”, Dokl. AN BSSR, 12:4, 293–297 | Zbl

[8] Sprindzhuk V. G., “Otsenki lineinykh form s $p$-adicheskimi logarifmami algebraicheskikh chisel”, Izv. AN BSSR. Ser. fiz.-matem. nauk, 1968, no. 4, 5–14 | Zbl

[9] Sprindzhuk V. G., “Effektivnye otsenki v “ternarnykh” pokazatelnykh diofantovykh uravneniyakh”, Dokl. AN BSSR, 13:9 (1969), 777–780 | Zbl

[10] Feldman N. I., “Otsenka lineinoi formy ot logarifmov algebraicheskikh chisel”, Matem. sb., 76(118) (1968), 304–319 | MR

[11] Feldman N. I., “Uluchshenie otsenki lineinoi formy ot logarifmov algebraicheskikh chisel”, Matem. sb., 77(119) (1968), 424–436

[12] Feldman N. I., “Odno neravenstvo dlya lineinoi formy ot logarifmov algebraicheskikh chisel”, Matem. zametki, 5:6 (1969), 681–689

[13] Feldman N. I., “Utochnenie dvukh effektivnykh neravenstv A. Beikera”, Matem. zametki, 6:6 (1969), 767–769

[14] Chebotarev N. G., Osnovy teorii Galua, ch. II, ONTI, M., L., 1937

[15] Shnirelman L. G., “O funktsiyakh v normirovannykh algebraicheski zamknutykh telakh”, Izv. AN SSSR. Ser. matem., 1938, no. 5–6, 487–498

[16] Adams W., “Transcendental numbers in the $p$-adic domain”, Amer. J. Math., 88:2 (1966), 279–308 | DOI | MR | Zbl

[17] Baker A., “Linear forms in the logarithms of algebraic numbers”, Mathematika, 13 (1966), 204–216 | MR | Zbl

[18] Baker A., “Linear forms in the logarithms of algebraic numbers. II”, Mathematika, 14 (1967), 102–107 | MR | Zbl

[19] Baker A., “Linear forms in the logarithms of algebraic numbers. III”, Mathematika, 14 (1967), 220–228 | MR | Zbl

[20] Baker A., “Linear forms in the logarithms of algebraic numbers. IV”, Mathematika, 15 (1968), 204–216 | MR | Zbl

[21] Baker A., “Contributions to the theory of Diphantine equation. I. On the representation of integers by bianary forms”, Philos. Trans. Royal Soc. London (A), 263:1139 (1968), 173–191 | DOI | MR | Zbl

[22] Baker A., “Contributions to the theory of Diophantine equation. II. The Diophantine equation $y^2=x^2+k$”, Philos. Trans. Royal Soc. London (A), 263:1139 (1968), 193–208 | DOI | MR | Zbl

[23] Baker A., “The Diophantine equation $y^2=ax^3+bx^2+cx+d$”, J. London Math. Soc., 43 (1968), 1–9 | DOI | MR | Zbl

[24] Baker A., “Bounds for the solutions of the hyperelliptic equations”, Proc. Cambridge Phil. Soc., 65 (1969), 439–444 | DOI | MR | Zbl

[25] Coates J., “An effective $p$-adic analogue of a theorem of Thue”, Acta Arithmetica, 15 (1969), 279–305 | MR | Zbl

[26] Hasse H., Zahlentheorie, Akademie Verlag, Berlin, 1963 | MR | Zbl

[27] Mahler K., “Zur Approximation algebraischer Zahlen. I”, Math. Ann., 107 (1933), 691–730 | DOI | MR | Zbl

[28] Mahler K., “Zur Approximation algebraischer Zahlen. II”, Math. Ann., 108 (1933), 37–55 | DOI | MR | Zbl

[29] Mahler K., “Zur Approximation algebraischer Zahlen III”, Acta Math., 62 (1934), 91–166 | DOI | MR | Zbl

[30] Mahler K., “Über die rationalen Punkte auf Kurven vom geschlecht Eins”, J. reins und angew. Math., 170 (1934), 168–178 | Zbl

[31] Thue A., “Über Annäherungswerte algebraischer Zahlen”, J. reine und angew. Math., 135 (1909), 284–305 | Zbl