The 11 references with contexts in paper P. Ivankov L., П. Иванков Л. (2016) “Уточнение некоторых оценок для значений гипергеометрических функций // Refinement of some estimates for values of the hypergeometric functions” / spz:neicon:technomag:y:2014:i:4:p:175-186

1
Galochkin A.I. [On the arithmetic properties the values of certain entire hypergeometric functions].Sibirskii matematicheskii zhurnal | Siberian mathematical journal, 1976, vol. 17, no. 6, pp. 1220{1235. (in Russian).
Total in-text references: 1
  1. In-text reference with the coordinate start=376
    Prefix
    ¡‡Ûχ̇ ¬‚‰ÂÌË œÂ‚ ̊ ӈÂÌÍË ÌÂÓ‰ÌÓÓ‰Ì ̊ı ÎËÌÂÈÌ ̊ı ÙÓÏ ÓÚ Á̇ ̃ÂÌËÈ „ËÔÂ„ÂÓÏÂÚË ̃ÂÒÍËı ÙÛÌ͈ËÈ Ò Ë‡ˆËÓ̇Π̧Ì ̊ÏË Ô‡‡ÏÂÚ‡ÏË · ̊ÎË ÔÓÎÛ ̃ÂÌ ̊ Ò ÔÓÏÓ ̆ ̧ ̨ ̋ÙÙÂÍÚË‚ÌÓÈ ÍÓÌÒÚÛ͈ËË ÎËÌÂÈÌ ̊ı ÔË·ÎËʇ ̨ ̆Ëı ÙÓÏ
    Exact
    [1]
    Suffix
    . ¬ ‡·ÓÚ [2] Ô‰ÎÓÊÂÌ ÌÂÍÓÚÓ ̊È ‚‡ˇÌÚ ÏÂÚÓ‰‡ «Ë„ÂΡ, ÍÓÚÓ ̊È ÔÓÁ‚ÓÎËÎ ÔÓÎÛ ̃ËÚ ̧ ‡Ì‡ÎÓ„Ë ̃Ì ̊ ӈÂÌÍË ‚ ·ÓΠӷ ̆ÂÈ ÒËÚÛ‡ˆËË. œË ̋ÚÓÏ ‚ Ó·ÓËı ÒÎÛ ̃‡ˇı · ̊ÎË ËÒÔÓÎ ̧ÁÓ‚‡Ì ̊ ҂‰ÂÌˡ ËÁ ÚÂÓËË ‰ÂÎËÏÓÒÚË ‚ ÔÓΡı ‡Î„·‡Ë ̃ÂÒÍËı ̃ËÒÂÎ.

2
Galochkin A.I. [Analogue of Siegel's method].Vestnik Moskovskogo universiteta. Ser. 1. Matematika, mekhanika, 1986, no. 2, pp. 30{34. (in Russian).
Total in-text references: 1
  1. In-text reference with the coordinate start=390
    Prefix
    ¡‡Ûχ̇ ¬‚‰ÂÌË œÂ‚ ̊ ӈÂÌÍË ÌÂÓ‰ÌÓÓ‰Ì ̊ı ÎËÌÂÈÌ ̊ı ÙÓÏ ÓÚ Á̇ ̃ÂÌËÈ „ËÔÂ„ÂÓÏÂÚË ̃ÂÒÍËı ÙÛÌ͈ËÈ Ò Ë‡ˆËÓ̇Π̧Ì ̊ÏË Ô‡‡ÏÂÚ‡ÏË · ̊ÎË ÔÓÎÛ ̃ÂÌ ̊ Ò ÔÓÏÓ ̆ ̧ ̨ ̋ÙÙÂÍÚË‚ÌÓÈ ÍÓÌÒÚÛ͈ËË ÎËÌÂÈÌ ̊ı ÔË·ÎËʇ ̨ ̆Ëı ÙÓÏ [1]. ¬ ‡·ÓÚÂ
    Exact
    [2]
    Suffix
    Ô‰ÎÓÊÂÌ ÌÂÍÓÚÓ ̊È ‚‡ˇÌÚ ÏÂÚÓ‰‡ «Ë„ÂΡ, ÍÓÚÓ ̊È ÔÓÁ‚ÓÎËÎ ÔÓÎÛ ̃ËÚ ̧ ‡Ì‡ÎÓ„Ë ̃Ì ̊ ӈÂÌÍË ‚ ·ÓΠӷ ̆ÂÈ ÒËÚÛ‡ˆËË. œË ̋ÚÓÏ ‚ Ó·ÓËı ÒÎÛ ̃‡ˇı · ̊ÎË ËÒÔÓÎ ̧ÁÓ‚‡Ì ̊ ҂‰ÂÌˡ ËÁ ÚÂÓËË ‰ÂÎËÏÓÒÚË ‚ ÔÓΡı ‡Î„·‡Ë ̃ÂÒÍËı ̃ËÒÂÎ.

3
Ivankov P.L. [Refinement of estimates for some nonhomogeneous linear forms].Matematicheskie zametki, 2005, vol. 77, iss. 4, pp. 515{521. (English translation:Mathematical Notes, 2005, vol. 77, iss. 3-4, pp. 476{481. DOI:10.1007/s11006-005-0046-7).
Total in-text references: 2
  1. In-text reference with the coordinate start=1031
    Prefix
    ŒÍ‡Á‡ÎÓÒ ̧, Ӊ̇ÍÓ, ̃ÚÓ ÛÔÓÏˇÌÛÚ ̊ ӈÂÌÍË ÏÓÊÌÓ ‚ ÌÂÍÓÚÓ ̊ı ÒÎÛ ̃‡ˇı ÛÚÓ ̃ÌËÚ ̧, ÔË ̃ÂÏ ̋ÚÓ ÛÚÓ ̃ÌÂÌË ÓÒÛ ̆ÂÒڂΡÂÚÒˇ Á‡ Ò ̃ÂÚ ÓÔÚËχΠ̧ÌÓ„Ó ‚ ̊·Ó‡ ÒÚÂÔÂÌË ÌÛÎÂ‚Ó„Ó ÏÌÓ„Ó ̃ÎÂ̇ ·ÂÁ Ô˂Π̃ÂÌˡ ÚÂÓÂÏ Ó ‰ÂÎËÏÓÒÚË ‚ ÔÓΡı ‡Î„·‡Ë ̃ÂÒÍËı ̃ËÒÂÎ
    Exact
    [3]
    Suffix
    . ÃÂÚÓ‰, ËÒÔÓÎ ̧ÁÓ‚‡ÌÌ ̊È ‚ ÔÓÒΉÌÂÈ ‡·ÓÚÂ, ÏÓÊÌÓ ÔËÏÂÌËÚ ̧ Ë ‚ ÒÎÛ ̃‡Â, ÍÓ„‰‡ ‡ÒÒχÚË‚‡ÂÏ ̊ ÌÂÓ‰ÌÓÓ‰Ì ̊ ÎËÌÂÈÌ ̊ ÙÓÏ ̊ ÒÓ‰ÂÊ‡Ú Ú‡ÍÊÂ Ë ÔÓËÁ‚Ó‰Ì ̊ ÒÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆Ëı ÙÛÌ͈ËÈ ÔÓ Ô‡‡ÏÂÚÛ.

  2. In-text reference with the coordinate start=1305
    Prefix
    ÃÂÚÓ‰, ËÒÔÓÎ ̧ÁÓ‚‡ÌÌ ̊È ‚ ÔÓÒΉÌÂÈ ‡·ÓÚÂ, ÏÓÊÌÓ ÔËÏÂÌËÚ ̧ Ë ‚ ÒÎÛ ̃‡Â, ÍÓ„‰‡ ‡ÒÒχÚË‚‡ÂÏ ̊ ÌÂÓ‰ÌÓÓ‰Ì ̊ ÎËÌÂÈÌ ̊ ÙÓÏ ̊ ÒÓ‰ÂÊ‡Ú Ú‡ÍÊÂ Ë ÔÓËÁ‚Ó‰Ì ̊ ÒÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆Ëı ÙÛÌ͈ËÈ ÔÓ Ô‡‡ÏÂÚÛ. «‡ÏÂÚËÏ Â ̆∏, ̃ÚÓ ÓˆÂÌÍË, ÔÓÎÛ ̃ÂÌÌ ̊ ‚ ‰‡ÌÌÓÈ ‡·ÓÚ (Í‡Í Ë ‚ ‡·ÓÚÂ
    Exact
    [3]
    Suffix
    ), ‚Ò  ̆ ‚ÂÒ ̧χ ‰‡ÎÂÍË ÓÚ ÓÊˉ‡ÂÏ ̊ı. 1. –ÂÁÛÎ ̧Ú‡Ú ̊ –‡ÒÒÏÓÚËÏ ÙÛÌ͈ËË Fklkj(z) = ∑∞ ν=0 zννj−1 ∏ν x=1 1 b(x) dlk dλlkk ∏ν x=1 1 x+λk , k= 1, . . . , t, lk= 0,1, . . . , τk−1, j= 1, . . . , u, (1) „‰Âb(x) = (x+β1). . .(x+βm)| ÏÌÓ„Ó ̃ÎÂÌ, ÔÂ‚ ̊Âv1−1ÍÓÌÂÈ ÍÓÚÓÓ„Ó ‡ˆËÓ̇Π̧Ì ̊ (v1>1), ‡(x+βv1). . .(x+βm)∈I[x];I| ÌÂÍÓÚÓÓ ÏÌËÏÓ ͂‡‰‡ÚË ̃ÌÓ ÔÓÎÂ;u=m+1; τ1, . . . ,τt| ̇ÚÛ‡Î ̧Ì ̊ ̃Ë

4
Ivankov P.L. [On linear independence of certain functions].Chebyshevskii sbornik, 2010, vol. 11, iss. 1, pp. 145{151. (in Russian).
Total in-text references: 2
  1. In-text reference with the coordinate start=2114
    Prefix
    ¡Û‰ÂÏ Ò ̃ËÚ‡Ú ̧, ̃ÚÓλ1, . . . ,λt| ‰Ó·Ì ̊ ‡ˆËÓ̇Π̧Ì ̊ ̃ËÒ·, ÔË ̃ÂÏλk1−λk2/∈ZÔËk16=k2,k1, k2= 1, . . . , t. œÓÚ·ÛÂÏ Ú‡ÍÊÂ, ̃ÚÓ· ̊ b(x)(x+λ1). . .(x+λt)Ì ‡‚ÌˇÎÓÒ ̧ ÌÛÎ ̨ ÔËx= 1,2, . . .œÂ ̃ËÒÎÂÌÌ ̊ ÛÒÎӂˡ Ó·ÂÒÔ ̃Ë‚‡ ̨Ú ÎËÌÂÈÌÛ ̨ ÌÂÁ‡‚ËÒËÏÓÒÚ ̧ ÙÛÌ͈ËÈ 1, Fklkj(z), k= 1, . . . , t, lk= 0,1, . . . , τk−1, j= 1, . . . , u,(2) ̇‰ ÔÓÎÂÏ ‡ˆËÓ̇Π̧Ì ̊ı ‰Ó·ÂÈ
    Exact
    [4, ÚÂÓÂχ 1]
    Suffix
    . “ÂÓÂχ 1.œÛÒÚ ̧06=ξ∈I,v=u−v1Ë ‚ ̊ÔÓÎÌÂÌ ̊ ‚Ò ÔÂ ̃ËÒÎÂÌÌ ̊ ‚ ̊ ̄ ÛÒÎӂˡ; ε| ÔÓËÁ‚ÓÎ ̧ÌÓ ÔÓÎÓÊËÚÂÎ ̧ÌÓ ̃ËÒÎÓ,h0,hklkj,k= 1, . . . , t,lk= 0,1, . . . , τk−1, j= 1, . . . , u, | ÌÂÚ˂ˇΠ̧Ì ̊È Ì‡·Ó ˆÂÎ ̊ı ̃ËÒÂÎ ËÁ ÔÓΡI.

  2. In-text reference with the coordinate start=15806
    Prefix
    »Á ̋ÚÓÈ ÎÂÏÏ ̊ ÛÚ‚ÂʉÂÌË ÚÂÓÂÏ ̊ ‚ ̊‚Ó‰ËÚÒˇ ıÓÓ ̄Ó ËÁ‚ÂÒÚÌ ̊Ï ÒÔÓÒÓ·ÓÏ; ÒÏ., ̇ÔËÏÂ, [10, Ò. 60]. «‡ÍÎ ̨ ̃ÂÌË ¬ÓÁÏÓÊÌÓÒÚË ÏÂÚÓ‰‡, ÔËÏÂÌÂÌÌÓ„Ó ‚ ‰‡ÌÌÓÈ ‡·ÓÚÂ, Ì ËÒ ̃ÂÔ‡Ì ̊. ƒ‡Î ̧ÌÂÈ ̄Ë ÂÁÛÎ ̧Ú‡Ú ̊ ÏÓ„ÛÚ · ̊Ú ̧ Ò‚ˇÁ‡Ì ̊ Ò Ó·Ó· ̆ÂÌËÂÏ ÚÂÓÂÏ ‡·ÓÚ ̊
    Exact
    [4]
    Suffix
    . «‰ÂÒ ̧, ÔÓ-‚ˉËÏÓÏÛ, ËÏ ̨Ú ÏÂÒÚÓ ÚÂÓÂÏ ̊ Ó ÎËÌÂÈÌÓÈ ÌÂÁ‡‚ËÒËÏÓÒÚË „ËÔÂ„ÂÓÏÂÚË ̃ÂÒÍËı ÙÛÌ͈ËÈ Ë Ëı ÔÓËÁ‚Ó‰Ì ̊ı (‚ ÚÓÏ ̃ËÒÎÂ Ë ÔÓ Ô‡‡ÏÂÚÛ) ̇‰ ÔÓÎÂÏ ‡ˆËÓ̇Π̧Ì ̊ı ‰Ó·ÂÈ, ÛÒÎӂˡ ÍÓÚÓ ̊ı ÒÓ‚Ô‡‰‡ ̨Ú Ò ÛÒÎӂˡÏË ÒÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆Ëı ÚÂÓÂÏ ‡·ÓÚ ̊ [11].

5
Ivankov P.L. [On differentiation with respect to parameter of some functions].Nauka i obrazovanie MGTU im. N.E. Baumana | Science and Education of the Bauman MSTU, 2012, no. 5. DOI:10.7463/0512.0398478(in Russian).
Total in-text references: 1
  1. In-text reference with the coordinate start=2613
    Prefix
    Œ·ÓÁ̇ ̃ËÏ H= max(|hklkj|, k= 1, . . . , t, lk= 0,1, . . . , τk−1, j= 1, . . . , u). “Ó„‰‡, ÂÒÎËH‰ÓÒÚ‡ÚÓ ̃ÌÓ ‚ÂÎËÍÓ (ÌËÊÌˇˇ „‡Ìˈ‡ Á‡‚ËÒËÚ ÓÚε), ÚÓ ‚ ̊ÔÓÎÌˇÂÚÒˇ ÌÂ‡‚ÂÌÒÚ‚Ó ∣ ∣ ∣ ∣ ∣ h0+ ∑t k=1 τk−1∑ lk=0 ∑u j=1 hklkjFklkj(ξ) ∣ ∣ ∣ ∣ ∣ > H −w−vv1−ε ,(3) „‰Âw=uT,T=τ1+. . .+τk. ¬
    Exact
    [5, ÚÂÓÂχ 3]
    Suffix
    ÔÓÎÛ ̃Â̇ ‡Ì‡ÎÓ„Ë ̃̇ˇ ÓˆÂÌ͇ ÎËÌÂÈÌÓÈ ÙÓÏ ̊, ÌÓ Ò Á‡ÏÂÌÓÈ ‚ ÔÓ͇Á‡ÚÂΠÒÚÂÔÂÌË ‚ Ô‡‚ÓÈ ̃‡ÒÚË (3) ‚ÂÎË ̃ËÌ ̊w+ v v1 ̇ u2T+mθ u−mθ , „‰Â θ= 1− 1 m ( 1 κ1 +. . .+ 1 κm ) , ‡κ1, . . . ,κm| ÒÚÂÔÂÌË ÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓ ̃ËÒÂÎβ1, . . . ,βm.

6
Ivankov P.L. [On the application of simultaneous approximations for the investigation of arithmetic properties of the values of hypergeometric functions].Nauka i obrazovanie MGTU im. N.E. Baumana | Science and Education of the Bauman MSTU, 2012, no. 12. DOI: 10.7463/1212.0500464(in Russian).
Total in-text references: 1
  1. In-text reference with the coordinate start=3269
    Prefix
    “Ó„‰‡w= 6,v= 2,v1= 1,θ= 1 2 Ë (4) ÔË‚Ó‰ËÚ Í ÌÂ‡‚ÂÌÒÚ‚Û8< 19 2 . 2. ƒÓ͇Á‡ÚÂÎ ̧ÒÚ‚‡ ƒÎˇ ‰Ó͇Á‡ÚÂÎ ̧ÒÚ‚‡ ÚÂÓÂÏ ̊ ÔËÏÂÌˇ ̨ÚÒˇ ÒÓ‚ÏÂÒÚÌ ̊ ÔË·ÎËÊÂÌˡ, ÍÓÚÓ ̊ ÒÚÓˇÚÒˇ Ò ÔÓÏÓ ̆ ̧ ̨ ÔË̈ËÔ‡ ƒËËıÎÂ, ıÓÚˇ ‚ ‡ÒÒχÚË‚‡ÂÏÓÏ ÒÎÛ ̃‡Â ÏÓÊÌÓ · ̊ÎÓ · ̊ ÔËÏÂÌËÚ ̧ Ë ̋ÙÙÂÍÚË‚ÌÛ ̨ ÍÓÌÒÚÛÍˆË ̨, ÒÏ.
    Exact
    [6]
    Suffix
    . œË ̋ÚÓÏ ÒÔˆˇΠ̧Ì ̊Ï Ó·‡ÁÓÏ ‚ ̊·Ë‡ÂÚÒˇ ÒÚÂÔÂÌ ̧ ÌÛÎÂ‚Ó„Ó ÏÌÓ„Ó ̃ÎÂ̇. Õ‡Ï ÔÓÚ·ÛÂÚÒˇ ˇ‰ ‚ÒÔÓÏÓ„‡ÚÂÎ ̧Ì ̊ı ÛÚ‚ÂʉÂÌËÈ. ÀÂÏχ 1.œÛÒÚ ̧N| ̇ÚÛ‡Î ̧ÌÓ ̃ËÒÎÓ,l| ÌÂÓÚˈ‡ÚÂÎ ̧ÌÓ ˆÂÎÓ ‡ˆËÓ̇Π̧ÌÓ ̃ËÒÎÓ.

7
ÿˉÎÓ‚ÒÍËÈ ¿.¡. Shidlovskiy A.B.Transtsendentnye chisla[Transcendental numbers]. Moscow, Nauka Publ., 1987. 448 p. (in Russian).
Total in-text references: 3
  1. In-text reference with the coordinate start=4650
    Prefix
    Aklks= 0,(6) „‰Â Aklks= n! s! dlk dλlkk n−s∏ x=1 1 λk+N1−n+x , k= 1, . . . , t, lk= 0,1, . . . , τk−1,06σ6N2(1−ε2)−1; ÔË ̋ÚÓÏ |θs|6eγ1n, s= 0,1, . . . , n.(7) ƒ Ó Í ‡ Á ‡ Ú Â Î ̧ Ò Ú ‚ Ó. –‡‚ÂÌÒÚ‚‡ (6) Ô‰ÒÚ‡‚Ρ ̨Ú ÒÓ·ÓÈ ÒËÒÚÂÏÛ ËÁ Ì ·ÓΠ̃ÂÏ n(1−ε2)Û‡‚ÌÂÌËÈ ÓÚÌÓÒËÚÂÎ ̧ÌÓn+ 1ÌÂËÁ‚ÂÒÚÌ ̊ı (5). œËÏÂÌËÏ ÎÂÏÏÛ «Ë„ÂΡ
    Exact
    [7, ÎÂÏχ 11, Ò. 109]
    Suffix
    . —̇ ̃‡Î‡ ÓˆÂÌËÏ Ó· ̆ËÈ Ì‡ËÏÂÌ ̧ ̄ËÈ Á̇ÏÂ̇ÚÂÎ ̧ ÍÓ ̋ÙÙˈËÂÌÚÓ‚ ‡ÒÒχÚË‚‡ÂÏÓÈ ÒËÒÚÂÏ ̊. ◊ËÒ·s(s−1). . .(s−σ+ 1)/σ!ˇ‚Ρ ̨ÚÒˇ ˆÂÎ ̊ÏË. ƒ‡ÎÂÂ, ËÒÔÓÎ ̧ÁÛˇ ÎÂÏÏÛ 1, ÔÓÎÛ ̃‡ÂÏ Aklks= n! s! n−s∏ x=1 (λk+N1−n+x) ∑±1 (λk+N1−n+x1). . .(λk+N1−n+xlk) .(8) Œ· ̆ËÈ Ì‡ËÏÂÌ ̧ ̄ËÈ Á̇ÏÂ̇ÚÂÎ ̧ ‰Îˇ ÏÌÓÊËÚÂÎÂÈ ÔÂ‰ ÒÛÏÏÓÈ ‚ Ô‡‚ÓÈ ̃‡ÒÚË ̋ÚÓ„Ó ‡‚ÂÌÒÚ‚‡ (ÔË ‚Ò‚ÓÁÏÓÊÌ ̊ı ‰ÓÔÛÒÚËÏ ̊ı Á̇ ̃ÂÌˡıkËs) ÓˆÂÌË‚‡ÂÚÒˇ

  2. In-text reference with the coordinate start=5375
    Prefix
    ◊ÚÓ· ̊ ‰Ó͇Á‡Ú ̧ ÔÓÒΉÌ ÛÚ‚ÂʉÂÌËÂ, ̇‰Ó Ò‡‚ÌËÚ ̧ ÒÚÂÔÂÌË, ‚ ÍÓÚÓ ̊ı ÔÓÒÚ ̊ ̃ËÒ· ‚ıÓ‰ˇÚ ‚ ̃ËÒÎËÚÂÎË Ë Á̇ÏÂ̇ÚÂÎË ‡ÒÒχÚË‚‡ÂÏ ̊ı ‰Ó·ÂÈ, ‡ Á‡ÚÂÏ ÔËÏÂÌËÚ ̧ ‡ÒËÏÔÚÓÚË ̃ÂÒÍËÈ Á‡ÍÓÌ ‡ÒÔ‰ÂÎÂÌˡ ÔÓÒÚ ̊ı ̃ËÒÂÎ. —ÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆ ‡ÒÒÛʉÂÌË ˇ‚ΡÂÚÒˇ Òڇ̉‡ÚÌ ̊Ï (ÒÏ., ̇ÔËÏÂ,
    Exact
    [7, ÎÂÏχ 2 Ò. 186]
    Suffix
    ). ’ÓÓ ̄Ó ËÁ‚ÂÒÚÌÓ, ̃ÚÓ Ó· ̆ ̇ËÏÂÌ ̧ ̄ Í‡ÚÌÓ ̃ËÒÂÎ1, . . . ,nÂÒÚ ̧ ‚ÂÎË ̃Ë̇ ÔÓˇ‰Í‡eO(n). ŒÚÒ ̨‰‡ ÌÂÚÛ‰ÌÓ ‚ ̊‚ÂÒÚË, ̃ÚÓ Ó· ̆ËÈ Ì‡ËÏÂÌ ̧ ̄ËÈ Á̇ÏÂ̇ÚÂÎ ̧ ‰Ó·ÂÈ, ‚ıÓ‰ˇ ̆Ëı ‚ ÒÛÏÏÛ ËÁ Ô‡‚ÓÈ ̃‡ÒÚË ‡‚ÂÌÒÚ‚‡ (8), Ì Ô‚ ̊ ̄‡ÂÚeγ3n.

  3. In-text reference with the coordinate start=9512
    Prefix
    N1−n∏ x=1 b(x) n! s! n−s∏ x=1 (λk+x) ∑lk μ=0 ( lk μ ) × × ( ∑±1 (λk+x1). . .(λk+xμ) ) dlk−μ dλlk−μk ∏n x=ν+1 (x+λk−s).(20) «Ì‡ÏÂ̇ÚÂÎ ̧ ‰Ó·Ë, ÒÓ‰Âʇ ̆ÂÈ Á̇ ̃ÂÌˡ ÏÌÓ„Ó ̃ÎÂ̇b(x), ÔÓÎÌÓÒÚ ̧ ̨ ÒÓÍ‡ ̆‡ÂÚÒˇ ‚ ÒËÎÛ ÛÒÎÓ‚ËÈ06ν < nËν+ 16s6n. –‡ˆËÓ̇Π̧ÌÓÒÚ ̧ ̃ËÒÂÎλkÔÓÁ‚ÓΡÂÚ, Í‡Í Ë ÔË ÓˆÂÌÍ ӷ ̆Â„Ó Ì‡ËÏÂÌ ̧ ̄Â„Ó Á̇ÏÂ̇ÚÂΡ ÏÌÓÊÂÒÚ‚‡ ̃ËÒÂÎ (8), ÔËÏÂÌËÚ ̧ ÒÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆Û ̨ Òڇ̉‡ÚÌÛ ̨ ÚÂıÌËÍÛ
    Exact
    [7, ÎÂÏχ 2, Ò. 186]
    Suffix
    . ƒÎˇ ÓˆÂÌÍË Ó· ̆Â„Ó Ì‡ËÏÂÌ ̧ ̄Â„Ó Á̇ÏÂ̇ÚÂΡ ÒÛÏÏ ̊ ‚ ÒÍӷ͇ı ÔËÏÂÌˇ ̨ÚÒˇ Ú Ê ÒÓÓ·‡ÊÂÌˡ, ̃ÚÓ · ̊ÎË ËÒÔÓÎ ̧ÁÓ‚‡Ì ̊ ‚ ‡Ì‡ÎÓ„Ë ̃ÌÓÈ ÒËÚÛ‡ˆËË ‰Îˇ ÒÛÏÏ ̊ ËÁ Ô‡‚ÓÈ ̃‡ÒÚË (8); ÒÏ. ‰Ó͇Á‡ÚÂÎ ̧ÒÚ‚Ó ÎÂÏÏ ̊2.

8
ÂÎ ̧‰Ï‡Ì Õ.». Fel'dman N.I.Sed'maia problema Gil'berta[Hilbert's seventh problem]. Moscow, MSU Publ., 1982. 312 p. (in Russian).
Total in-text references: 1
  1. In-text reference with the coordinate start=10843
    Prefix
    ÌÂÎ ̧Áˇ ÛÚ‚Âʉ‡Ú ̧, ̃ÚÓσ6N2(1− ε2)−1, Ú‡Í Í‡Í ÌÂ‡‚ÂÌÒÚ‚Óν>N3ËÁ ÎÂÏÏ ̊3Ì ‚ ̊ÔÓÎÌˇÂÚÒˇ. œÓ ̋ÚÓÏÛ Ì‡‰Ó Á‡ÏÂÌËÚ ̧ ‚ÂıÌ ̨ ̨ „‡ÌËˆÛ ËÁÏÂÌÂÌˡσ‚ Ô‡‚ÓÈ ̃‡ÒÚË (14) ̇N4, „‰ÂN4| ÒÚÂÔÂÌ ̧ ÏÌÓ„Ó ̃ÎÂ̇ Qkμ2jν(s). œÓÒÍÓÎ ̧ÍÛ (14) ˇ‚ΡÂÚÒˇ ‡ÁÎÓÊÂÌËÂÏ ÏÌÓ„Ó ̃ÎÂ̇ ËÁ ΂ÓÈ ̃‡ÒÚË ̋ÚÓ„Ó ‡‚ÂÌÒÚ‚‡ ‚ ˇ‰ Õ ̧ ̨ÚÓ̇, ÚÓ Á‰ÂÒ ̧ ÏÓÊÌÓ ËÒÔÓÎ ̧ÁÓ‚‡Ú ̧ „ÓÚÓ‚ ̊ ÙÓÏÛÎ ̊ ÒÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆ÂÈ ÚÂÓËË (ÒÏ., ̇ÔËÏÂ,
    Exact
    [8, Ò. 40-41]
    Suffix
    ). œÓ‰ÒÚ‡‚ËÏ ÚÂÔÂ ̧ (14) Ò Û ̃ÂÚÓÏ (21) ‚ ÔÓÒΉÌ ‚ ̊‡ÊÂÌË ËÁ ̃ËÒ· ‚ıÓ‰ˇ ̆Ëı ‚ (12), ÓÚ·ÓÒË‚ ÔË ̋ÚÓÏ ÌÛ΂ ̊ Ò·„‡ÂÏ ̊Â. “‡ÍÓ‚ ̊ÏË ‚ ÒÓÓÚ‚ÂÚÒÚ‚ËË Ò ÎÂÏÏÓÈ2·Û‰ÛÚ ÚÂ, Û ÍÓÚÓ ̊ıσ6N2(1−ε2)−1. ¬ ÂÁÛÎ ̧Ú‡Ú ÔË06ν6N1−1ÔÓÎÛ ̃ËÏ Ú‡ÍÓ ‡‚ÂÌÒÚ‚Ó: S1= n!

9
Chudnovsky D.V., Chudnovsky G.V. Applications of Pad-e approximation to diophantine inequalities in values of G-function. In:Number Theory. Springer Berlin Heidelberg, 1985, pp. 9{51. (Ser.Lect. Notes in Math.; vol. 1135). DOI:10.1007/BFb0074600
Total in-text references: 2
  1. In-text reference with the coordinate start=14019
    Prefix
    Rw(z)    , „‰Â ÍÓÏÔÓÌÂÌÚ ̊ ÒÚÓηˆÓ‚P(z)ËR(z)ÒÛÚ ̧ ÒÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆ËÏ Ó·‡ÁÓÏ ÔÂÂÌÛÏÂÓ‚‡ÌÌ ̊ ÏÌÓ„Ó ̃ÎÂÌ ̊ (16) Ë ÙÛÌ͈ËË (15). “Ó„‰‡ R(z) =P(z)F(z) +P(z). ƒ‡Î ̧ÌÂÈ ̄Ë ‡ÒÒÛʉÂÌˡ ÔÓ‚Ó‰ˇÚÒˇ ÔÓ ÒıÂÏÂ, Ô‰ÎÓÊÂÌÌÓÈ ‚ ‡·ÓÚÂ
    Exact
    [9]
    Suffix
    . œÓÎÓÊËÏ Rq(z) =zq(D−A)qR(z), q= 0,1, . . . , „‰ÂD= d dz | ÓÔÂ‡ÚÓ ‰ËÙÙÂÂ̈ËÓ‚‡Ìˡ. flÒÌÓ, ̃ÚÓ Rq(z) =Pq(z)F(z) +Pq(z), „‰Â Pq(z) =zq dq dzq P(z), ‡Pq(z)ÂÒÚ ̧ ÒÚÓηˆ ‚ ̊ÒÓÚ ̊w, ÒÓÒÚ‡‚ÎÂÌÌ ̊È ËÁ ÏÌÓ„Ó ̃ÎÂÌÓ‚; ÍÓÏÔÓÌÂÌÚ ̊ ̋ÚÓ„Ó ÒÚÓηˆ‡ Ó·ÓÁ̇ ̃ËÏP1q(z), .

  2. In-text reference with the coordinate start=14309
    Prefix
    , „‰ÂD= d dz | ÓÔÂ‡ÚÓ ‰ËÙÙÂÂ̈ËÓ‚‡Ìˡ. flÒÌÓ, ̃ÚÓ Rq(z) =Pq(z)F(z) +Pq(z), „‰Â Pq(z) =zq dq dzq P(z), ‡Pq(z)ÂÒÚ ̧ ÒÚÓηˆ ‚ ̊ÒÓÚ ̊w, ÒÓÒÚ‡‚ÎÂÌÌ ̊È ËÁ ÏÌÓ„Ó ̃ÎÂÌÓ‚; ÍÓÏÔÓÌÂÌÚ ̊ ̋ÚÓ„Ó ÒÚÓηˆ‡ Ó·ÓÁ̇ ̃ËÏP1q(z), . . . ,Pwq(z). ƒ‡ÎÂÂ, ‡ÒÒÛʉ‡ˇ, Í‡Í ‚
    Exact
    [9]
    Suffix
    , ÛÒÚ‡ÌÓ‚ËÏ, ̃ÚÓ ÔË ‰ÓÒÚ‡ÚÓ ̃ÌÓ ·ÓÎ ̧ ̄ÓÏnÙÛÌ͈ËÓ̇Π̧Ì ̊È ÓÔ‰ÂÎËÚÂÎ ̧, ÒÚÓ͇ÏË ÍÓÚÓÓ„Ó ÒÎÛʇÚPq(z),P1q(z), . . . , Pwq(z),q= 0,1, . . . , w, ÓÚÎË ̃ÂÌ ÓÚ ÚÓʉÂÒÚ‚ÂÌÌÓ„Ó ÌÛΡ; ÒÔ‡‚‰ÎË‚ÓÒÚ ̧ ÔÓÒΉÌÂ„Ó ÛÚ‚ÂʉÂÌˡ Ó·ÂÒÔ ̃Ë‚‡ÂÚÒˇ ÎËÌÂÈÌÓÈ ÌÂÁ‡‚ËÒËÏÓÒÚ ̧ ̨ ÙÛÌ͈ËÈ (2) ̇‰ ÔÓÎÂÏ ‡ˆËÓ̇Π̧Ì ̊ı ‰Ó·ÂÈ.

10
ÌÍÓ‚ œ.À. Ivankov P.L. [On linear independence of values of entire hypergeometric functions].Sibirskii matematicheskii zhurnal| Siberian mathematical journal, 1993, vol. 34, no. 5, pp. 53{62. (in Russian).
Total in-text references: 1
  1. In-text reference with the coordinate start=15638
    Prefix
    ˆÂÎ ̊ÏË ‚ ÔÓÎÂI, ‡ ÏÓ‰ÛÎ ̧ Ó· ̆Â„Ó Ì‡ËÏÂÌ ̧ ̄Â„Ó Á̇ÏÂ̇ÚÂΡ ÓÒڇΠ̧Ì ̊ı ̃ËÒÂÎ ËÁ (26) ÓˆÂÌË‚‡ÂÚÒˇ Ò‚ÂıÛ ‚ÂÎË ̃ËÌÓÈeγ12n(n!) v v1T; 3)|g (q) 0fr(ξ) +g (q) r|6(n!) −u(1−ε4)v1T ,r= 1, . . . , w, ÂÒÎËn‰ÓÒÚ‡ÚÓ ̃ÌÓ ‚ÂÎËÍÓ; 4)|g (q) 0|6e γ13n(n!)u; ‰‚‡ ÔÓÒΉÌËı ÌÂ‡‚ÂÌÒÚ‚‡ ÒÔ‡‚‰ÎË‚ ̊ ÔËq= 0,1, . . . , w. »Á ̋ÚÓÈ ÎÂÏÏ ̊ ÛÚ‚ÂʉÂÌË ÚÂÓÂÏ ̊ ‚ ̊‚Ó‰ËÚÒˇ ıÓÓ ̄Ó ËÁ‚ÂÒÚÌ ̊Ï ÒÔÓÒÓ·ÓÏ; ÒÏ., ̇ÔËÏÂ,
    Exact
    [10, Ò. 60]
    Suffix
    . «‡ÍÎ ̨ ̃ÂÌË ¬ÓÁÏÓÊÌÓÒÚË ÏÂÚÓ‰‡, ÔËÏÂÌÂÌÌÓ„Ó ‚ ‰‡ÌÌÓÈ ‡·ÓÚÂ, Ì ËÒ ̃ÂÔ‡Ì ̊. ƒ‡Î ̧ÌÂÈ ̄Ë ÂÁÛÎ ̧Ú‡Ú ̊ ÏÓ„ÛÚ · ̊Ú ̧ Ò‚ˇÁ‡Ì ̊ Ò Ó·Ó· ̆ÂÌËÂÏ ÚÂÓÂÏ ‡·ÓÚ ̊ [4]. «‰ÂÒ ̧, ÔÓ-‚ˉËÏÓÏÛ, ËÏ ̨Ú ÏÂÒÚÓ ÚÂÓÂÏ ̊ Ó ÎËÌÂÈÌÓÈ ÌÂÁ‡‚ËÒËÏÓÒÚË „ËÔÂ„ÂÓÏÂÚË ̃ÂÒÍËı ÙÛÌ͈ËÈ Ë Ëı ÔÓËÁ‚Ó‰Ì ̊ı (‚ ÚÓÏ ̃ËÒÎÂ Ë ÔÓ Ô‡‡ÏÂÚÛ) ̇‰ ÔÓÎÂÏ ‡ˆËÓ̇Π̧Ì ̊ı ‰Ó·ÂÈ, ÛÒÎӂˡ ÍÓÚÓ ̊ı ÒÓ‚Ô‡‰‡ ̨Ú Ò ÛÒÎӂˡÏË ÒÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆Ëı Ú

11
Galochkin A.I. On effective bounds for certain linear forms. In:New Advances in Transcendence Theory. Cambridge, Cambridge Univ. Press, 1988, pp. 207{215.
Total in-text references: 1
  1. In-text reference with the coordinate start=16059
    Prefix
    «‰ÂÒ ̧, ÔÓ-‚ˉËÏÓÏÛ, ËÏ ̨Ú ÏÂÒÚÓ ÚÂÓÂÏ ̊ Ó ÎËÌÂÈÌÓÈ ÌÂÁ‡‚ËÒËÏÓÒÚË „ËÔÂ„ÂÓÏÂÚË ̃ÂÒÍËı ÙÛÌ͈ËÈ Ë Ëı ÔÓËÁ‚Ó‰Ì ̊ı (‚ ÚÓÏ ̃ËÒÎÂ Ë ÔÓ Ô‡‡ÏÂÚÛ) ̇‰ ÔÓÎÂÏ ‡ˆËÓ̇Π̧Ì ̊ı ‰Ó·ÂÈ, ÛÒÎӂˡ ÍÓÚÓ ̊ı ÒÓ‚Ô‡‰‡ ̨Ú Ò ÛÒÎӂˡÏË ÒÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆Ëı ÚÂÓÂÏ ‡·ÓÚ ̊
    Exact
    [11]
    Suffix
    . —ÔËÒÓÍ ÎËÚÂ‡ÚÛ ̊ 1.√‡ÎÓ ̃ÍËÌ ¿.». Œ· ‡ËÙÏÂÚË ̃ÂÒÍËı Ò‚ÓÈÒÚ‚‡ı Á̇ ̃ÂÌËÈ ÌÂÍÓÚÓ ̊ı ˆÂÎ ̊ı „ËÔÂ„ÂÓÏÂÚË ̃ÂÒÍËı ÙÛÌ͈ËÈ // —Ë·ËÒÍËÈ Ï‡ÚÂχÚË ̃ÂÒÍËÈ ÊÛ̇Î. 1976. “.17, π 6. —. 1220{1235. 2.√‡ÎÓ ̃ÍËÌ ¿.