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㒿िᤌ 枼& * - -DFREL &DUO *XVWDU -DFRE 1804 12 ᗙ 10 ᔐύᓴჇି⡩୭ 柋1851 2 ᗙ 18 ᔐ࣯ᓴᙣᙀ ώᓄ ฎ ώ
㒿िᤌלݴⷍध㐩 7KH 0DF7XWRU +LVWRU\ RI 0DWKHPDW LFV DUFKLYH ┐⌴
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فம⌋㓾ᔷ⇩⍭ዷ
㒿िᤌ 枼& * - -DFREL &DUO *XVWDU -DFRE 1804 12 ᗙ 10 ᔐύᓴჇି⡩୭ 柋1851 2 ᗙ 18 ᔐ࣯ᓴᙣᙀ ώᓄ ฎ ώ
㕂মᖺẘ㌛ⲟວ⧙ 㕂ম 6LPRQ -DFREL ਘڒ⃞
⥿ᙃ /HKPDQQ ⃞⏜٩ݗࡁ ц㕂মᙌتݗ㒆ڒد᤺⃞
⤺㊞⣢ 0RULW] 栾ᄞ܊ா✃ᄐᄣ⦰ু⃞Ḏἱວ цკკ
ሬᄹ⥩ (GXDUG ா࡚ᷫঔغᄞᏘ٦㌛ⲟ цڒㆧᙌݗൎൎ㕧ᰲ
7KHUHVH ц
㕂ম⠇ၪ✍ᔚ 栾ၪၣ㔮ڒ⠚⠚⚫ፕثᕄਘᔷ ц1816 ၣ 11 ᙋㅪࡏᩂ⣢ೲ㘟⌋⚫ ц1821 ၣᖳ“ ц‧ᗆڒ⃞သ⟷
⸩ хፕث⸩ਘ⃞◯ㇺᄚࠣ‥ 桍࡚ாᔷᕥ㖭 栾ڒᏘᐙ⃞
⇉⺼ㆉㆉ⾰ㅻᜉዷᔢᏕ⃞ࡐຩ цڒㆧ⠇٦ / ᤦፕ (XOHU ⃞ ъᴸ⎔࢛ᚬდ⹐ы,QWURGXFWLR LQ DQDO\VLQ LQILQLWRUXP 栾ؿظ⸂
ழⶫٯᤄڜᔷᕥ⌫ ц
1821 ၣ 4 ᙋ㕂মࡏᛕᚲೲ ц㒑൝ࡒၣ⃞⚫ῳ᪃ 栾ڒ
ਖ਼ хতᕄਘᔷㇺ㘤ᙌ⠜⿄ ц⸋ᜉᜉ㒆ⷷ߿⸲ 栾ᄨت㒑
൝ 栾㕂ম㙝⊡ڒᖺتݗ ³ࡑጁ´ цߡ & ) 㞖ᕞ *DXVV ت ᡥ 栾سᖺᔷშᴀৠდ⦰ڒ 栾ڒᄚম❫ா⸩ⷁذঝᄣᄚ㞖
ц㕂মᙆᄞㆧᖺ᧳ຖࡑࣸጶゎᕧᔷ ц1825 ၣ 8 ᙋ 栾ڒỂ ᄣᛕᚲೲἱॡೕۗ цِᄞ 栾‖ᜉکᔢ ц1825 ၣࢲ 1826 ၣ
ࡲ 栾ڒى⺋㓊ᕧد▂⍰㒙ᘻ▤ਘᘻ㖭⃞ⶫᚬἱ⹐⸵⌫ цၣߘ٩
॒ت᤺⃞㕂মળᕧໜ⠇တ⃞ᕟ㦼⽅⍴ாᔢِف 栾ટ⃘ῳẺ
⎧ᅼ⛑ 栾ᖺ‧ᗆᙆৠდڂ⃞ᔷᔢဳ цڒ⃞ࣹდ⾨ᗣ㟹ೕᔢ✹
⃞ᩆሣ ц
1826 ၣ 5 ᙋ 栾㕂মࢲᛯᕞೲکᔢ цாㆽⴂڒ╁⺼٦ Ḏἱວ ) ڳᙃ 1HXPDQQ ਘ + ೬⽒ 'RYH хᔷວ ) ဓ
౻⛱ %HVVHO цتၣِᄞ 栾⃘ⲯ٦ၬ㓊ᕧᔷ⹐فᙌ㓊٭ছᄝ ᄞ
ڂ⍄ ³㕂ম⏘⬭⃞٭ছᄝ´ ⃞⹐ᕄ 栾ঞࢲ㞖ᕞ⃞⻩⽫ ц ᤴ
㒑൝ᔷࣝۦ⃞㦫㊣ᗆڜ ц1827 ၣ 12 ᙋỂᄣࣚᔢᏕ✓ۗ 栾ㅚ ᤄᐋॖ⠛㞖ᕞ х$ 0 ए⻣ᄹ /HJHQGUH ڒᖆᙛဉۦ⃞⻩ᐓᙌ
㓊 ⛘㞖ᕞسᖺتݗハᖨⲯቊ⃞ڂ ц1829 ၣ⃘ⲯ٦ڒ⃞⏜ت
ۦъᢐலᔷἱ⹐ᕟళ⊃ы)XQGDPHQWD 1RYD 7KHRULD )XQFWLRQXP
(OOLSWLFDUXP 栾1892 栾ъ㕂মࡑ㕃ы⏜تॲ цীၣೳ㕂
মঔဓ㦯ᕮⲟ 栾ㅖفⷛક٦ாث⃞㞖ᕞ 栾ؿ╁⺼٦ए⻣
ᄹ х- % - ޯ㊞⦦ )RXULHU х6 ' ᨮ 3RLVVRQ ਘ࡚ڒᨷமᔷ
ວ ц1832 ၣ 7 ᙋⳝᐋॖᔢᏕ цாᤴࣆتၣ 栾९ 1831 ၣ 9 ᙋ 11 ᖃ⠛㛦㊞⛴ ᕨ࠽ 0DULH 6FKZLQFN ╁ල 栾ڒݜῳᙌٯݗࡁ
ਘدݗഞࡁ ц1842 ၣ 7 ᙋঞᗣ㟹ೕமộ⃞᪆ㆌ 栾ਘဓ౻⛱কࣺ
ாᙃᄺᕞḚ⠝ⲟ⃞سࢧ㙏⌋ܬㅪय़ᙈ %ULWLVK $VVRFLDWLRQ IRU WKH
$GYDQFHPHQW RI 6FLHQFH ⃞ၣᙈ 栾மㅖفாဓ㦯⌋㓾ۦ٦
৮ ц
ாᛯᕞೲ⃞॒ࡔၣ㒙 栾㕂মس⇉⁉ݯဉۦ⦰ 栾ா⌋
⇩⍭ਘᔢذㇺސ㝪ڂ⃞◯ цڒᢐலᔷἱ⹐⃞ㅓᄺ⇩⍭
ாᔷ‐დ⾨ㄊऑ 栾ᄨ⛘⠛ 1 + 㓨⼹ᷱ $EHO 㨊ু ц㕂মா
ᢐலᔷἱ⹐ хᔷ࢛ᚬ хᔷ⹐ хၬ۟ хࣸᕥ㖭⃞ى⹐
ᕄㇺ⃘ⲯா࠽ࢧᷱ⃞ъ┓ⓔਘኩΌᔷы㕖⸞ &UHOOH¶V -RXUQDO IU GLH UHLQH XQG DQJHZDUGWH 0DWKHPDWLN ذ 栾ၢᙛᙌد㕂ম
⃞ᕄ⎮ цㅚ܃ڒᄚᅚỂᄣம㔦✏⻔ цڒسݯ⃞⇩⍭ဉۦؿᨈ ᙌᄉ㘐ڒ⃞ᔢ᪃ऑ цㅩΌ 8 ± 10 ᗆ═ῳ⺋ⶫڒሬ⃞
⸵⌫ ² ᢐலᔷἱ⹐ 栾ؿໜ⠇တ⃞⇩⍭ⓙ㞒ᔢ═ῳ 栾܃ῳ
ঞࢲ⌋⇩⃞⪫㔌 栾ጆ⇿٦္⃞ᔢᕥᨷ цڒㆧ㒑ࣝ٦ⲣⷉ⹐
栾ㅚா‧ᗆᔷ‐ㆧᖺᄚᕟം⃞٨Ḏ ц‧ᗆ 栾ڒীᔷວဓ౻
⛱ хḎἱວ ) ڳᙃدڂᄹமᔷᄯ⠜⃞ᅂ ц
1843 ၣࢩ㕂মᇕ٦㊟⃞ⓦ⁙ цாᄣࢲᗣ㟹ೕமộ⃞Ꮁᤗ
ِᄞঔ⚉ೲࢯڹރᔷᙋ ц1844 ၣ 6 ᙋၸࢲᛕᚲ 栾㒑൝Ꮾঞᗣ㟹
ೕமộ⃞ᩮ⽓ 栾ாᛕᚲೲکᔢ 栾ؿⳝ㆛ᛕᚲ⌋㓾㓾ೕ хݴ ᔪ⃠ວᙈᙈੌ ц
1848 ၣ㖰ᙛ㒙 栾 ᕧڒாتᤄ९ဴᯊ⺋فᄣ♚٦ộປ⛘ঔ
ᩮ⽓ ц‧▂ٜ┌ೲ᧳ຖ✄⹈ڒᗆ 栾ᗣ㟹ೕ‧ሣ⺼ࢲڒ⃞㕛㒑 ໜᙈㅡ⃞ᐳ 栾ங⛘ᆪᄯ٦ڒ⃞ᄗㅶ ц
1851 ၣࢩ㕂মாᇕ᪉ⲟᆄሯࡦㆧᙣ⁛₾ᗆ 栾খᄣ٦ೳ⢔ 栾 سٍঔغ цڒ⃞ັঙ 3 * / Ṏࢯ࠽㕧 'LULFKOHW ாᛕᚲ⌋㓾⃘
ⲯ⓿ᅡ⺋⸊ 栾◮╁٦ڒாᔷذ⃞⼽ỉ 栾⍄ڒ - / ፕᙖ ᖃ /DJUDQJH ڞ܊⌋㓾ੌفᙆफ़⾲⃞ᔷວ ц
㕂মᙆ㊟⃞⼽ỉᖺਘ᎑ඊᔷວ 1 + 㓨⼹ᷱ $EHO ℩
٭Ẻ⎧ࣝ⎧ਘ⃘།٦ᢐலᔷἱ⹐ 桍დࡏؿ⇩⍭٦ θ ᔷਘ࡚
تٲ⾰⾲ᔷ⃞ᆄ⽶ 桍ೲ⟣܃Όⴜᔷ 栾⃘།٦ⴜ⻝㊡ᢐல
ᔷ цڒ⃞⏜تۦъᢐலᔷἱ⹐ᕟళ⊃ы⸋㘥ఝ⃞╲⦰
ۦ ц⸋⦰ۦ⃞⏜ت࢛⇩⍭⻝ᐔક㙃 栾⏜٩࢛═ᢐலᔷ⃞
ⲯ⊡ цா⏜ت࢛ 栾㕂মᄨ⏜ت㙒ᢐலᔷ⃞ᄴ⃘࢛ 栾Ό٩ ᤄ⻝ᐔໜ⑹ऺए⻣ᄹ⃞ᡞ᭭ჽ цڒ⇩⍭٦ᙌἱ⻝ᐔ y = u
v فᔷ u ި ਘ v ം ⃞ᆄ⽶ 栾ؿ═٦دᤄਘٯᤄ⻝ᐔ⃞ਘ ᙌ㓊ᡤᕥ⌫⃞ ц╲┺়ࡒݗ⻝ᐔ 栾ڒᄣࢲ٦⏜ت㙒ᢐல⍕࢛
⃞ٗᨷࡕ цڒᎁ 栾ໜছᔷ ϕ = amu დㅪᢐல⍕࢛
t(ϕ, k) = Z ϕ
0
dϕ
p1 − k2 VLQ2 ϕ 栾
ㅚⴂ x = VLQϕ = VLQamu 栾ᵃᄞ FRVamu = am(k − u) ㅚⴂ
k = u[π
2 , k] 栾ࣁᄣࢲ
∆amu = p
1 − k2 VLQ2 amu ц
ᤴڒᏰೲ㊡ࡕ цࢯΌ⬪⻝ᐔ VLQϕ = iWDQϕ ڒჃ⎧٦㓊ܫ
VLQam(iu, k) = iWDQam(u, k′) 栾
ㅚⴂᡤᔷ k ਘ k′ ᮹⿏ᕥ⌫ k2 + k′2 = 1 цㅚᡥ 栾ڒᄣࢲᢐலᔷ
⃞㕓ㅩᙛᆄ х㕦㦼 х៰㦼 цڒㆧ⺯ᖣ‧⏜تݗᡤᔷਘ⏜٩ݗᡤ ᔷኩΌীᡥ⻝ᐔᗆᡤᕥ⌫⃞س⻝ᆄ ц⏜ت࢛ဉۦ⃞ᙆᄞ 栾ڒ⇩
⍭٦᮹⿏ዷᙌ⻝ᐔᡤᔷ⃞د㔝ᄴ࢛ᕥ⌫ ц
ㅚ⦰ۦ⃞⏜٩࢛㕃ف⇩⍭ᢐலᔷΌᴸ⎔┙ᔷٗ⍕ਘޯ㊞⦦┙
ᔷ⃞ⲯ⊡ક㙃 цᢐலᔷ VLQamu хFRVamu х∆amu ⃞⏜ت⍁
ⲯ⊡ᖺΌᴸ⎔ٗ⍕⃞એჽ═ цⷒ q = e−πK′K 栾㕂মΌ q ܊ ⲯ⊡ᡤਘㅩᙛ 栾ഫ
k = 4√ q
(1 + q2)(1 + q4)(1 + q6)· · · (1 + q)(1 + q3)(1 + q5)· · ·
4 ц ᢐலᔷㆧমΌޯ㊞⦦┙ᔷ།㒑܊ⲯ⊡ ц
㕂মდㅪᔷ
Z(u) = F1(u) − E1(u)
F1 (ϕ = amu)
܊ⷉ⹐⏜٩㙒ᢐல⍕࢛ цڒໜ⏜د㙒ᢐல⍕࢛ऺ⑹⏜ت㙒ਘ⏜٩ 㙒ᢐல⍕࢛ 栾⛘⏜دݗ⾰⾲ᔷߘܜ⽽ᕧࡒݗ⻝㊡ цڒখდࡏ ³㕂 মᔷ´
Θ(u) = Θ(0) · H[SZ u 0
Z(u)du
ਘᔷ H(u) ܃ᄣ VLQamu = 1√ k ·
H(u)
Θ(u) цㅚⴂ Θ(u) ਘ H(u) ⲯ
⊡ᴸ⎔ٗ⍕ਘޯ㊞⦦┙ᔷ ц ᢐலᔷ⠛ Θ ᔷِ㒙㓊ܫমᄣ
ࢲڞر⃞⦰ুࡕ
r2kK
π = 2√4 q + 2p4
q9 + 2p4
q25 + 2p4
q49 + · · · ц 㕂মখໜㅚဉۦኩΌᕧᔷ⹐ цᄨᆙ⏯
2K π
2
= (1 + 2q + 2q4 + 2q9 + 2q16 + · · ·)4
= 1 + 8X
ϕ(p)(qp + 3q2p + 3q4p + 3q8p + · · ·) 栾
࡚ف ϕ(p) ᖺംᔷ p ⃞ஙᔷِਘ 栾ڒ⺯ᖣ٦ᙌু⃞⽒㛦 )HUPDW
⹐ᕣ 栾९ک۟ᔳᔷমڞⲯ⊡⠌கݗᔳᔷ 㕦ٜᖺᔳᔷ ⃞ၢᕥ ਘ ц
㕂ম⺯ᖣ٦ڞ e−an+b2 ㅛ㘖⃞┙ᔷ⃞ᔉᕀᆄ 栾ㅚᖺᔳݗᢐல
ᔷἱ⹐⃘།⃞ళ⊃ ц
1829 ± 1830 ၣࡲ 栾㕂মڒ⏜تᤄۦᢐலᔷἱ⹐⃞
৮ 栾ڒშ⸾㕓ㅩᙛᆄᖺᢐலᔷ⃞ళᙥᆄ⽶ цڒΌ θ ᔷἱ⹐܊
Ⴣ⎧ᢐலᔷἱ⹐ ц1835 ± 1836 ၣ 栾ڒ⺯ᖣᙌ㓊கݗ θ ᔷٗ
⍕ِਘ⃞⦰ুຖἱ 栾ؿظໜহ㙒ᢐலຖ⚉ θ ᔷِએ 栾ᄨ⛘
⏜تݗࣝ⎧٦ θ ᔷἱ⹐ ц1839 ± 1840 ၣᙛ㒙 栾ڒ☟☪ㅚٲ⇩
⍭ 栾ㅚ࢛ဉۦᔉ㕃ாъ㕂মࡑ㕃ы⃞⏜ت㕃 х⏜٩㕃ف 栾भ
፩٦ᢐலᔷ⃞៷ㄼ ц
㓊ᕧⴜ⻝㊡ᢐலᔷἱ⹐ 栾ڒ⇩⍭٦⾰ᢐல⍕࢛⏯ક㙃 栾࡚ف ᙌ㓊㕓ㅩᙛᔷ⃞⹐ᕄ 1835 ၣ Ἢڜⴜ⻝ᔷἱ⹐ف⃞╲⦰
ۦ цڒ㓨⼹ᷱᔷٜۦㅻ⇩⍭ 栾⃘Ἢ٦⾰ᢐலᔷ ц
ாᢐலᔷἱ⹐⃞ᔳݗ⃘།ㅻ⌫ف 栾㞖ᕞ хए⻣ᄹ х㓨⼹
ᷱ х㕂মڒݜ࡚ἱ⹐ㇺۦㅻⓙᅂ⇩⍭ ц㓨⼹ᷱਘ㕂ম⃞
೬⃘Ἢী㞖ᕞၣ㖤ᗆ 1798 ၣ ۦㅻ⃞ےᨈᙌ⃘ⲯ⃞ဉۦ 㞖ᕞᄨ܊
سாْڒ⃞⇩⍭⹐ᕄ⃞⃘ⲯ ℩ٷ″ цए⻣ᄹ⠇ 1786 ၣڞ܊Ό
٦க॒ၣᗆ㒙ᢐல⍕࢛ۦ٦⓼╚⃞⇩⍭ 栾ؿໜ࡚࢛د㙒 цے 㓨⼹ᷱਘ㕂মℷࢲ٦ક㙃⃞້⽶ 栾ڒݜጮए⻣ᄹ⃞ᅼ⿾ݝㅻ
܊ 栾⇩⍭ᢐல⍕࢛⃞ㅎ 栾९ᢐலᔷ 栾ㅚᡥೲೲ⑹ऺ٦ᔳݗ ક㙃 栾܃ᄣᢐலᔷἱ⹐ㄢẅ⃘།⾨܊ ц
ᢐலᔷἱ⹐ா॒ٚغ⓿ᔷ㘥ఝف۞ᙌ॒࢛㊟⃞ۗ ц
⃘Ἢਘᔌㅪⴜ⻝ᔷἱ⹐ف⃞ت⠴ຖἱࣝㅡ٦ᙌࢯڧ цഫᚶ ᨈᙌᢐலᔷἱ⹐ف⃞تٲḚⴜ⻝ᔷἱ⹐ᐋܚㆽ㦧೬⃞▤
┡ 栾ㆽ㦧ⴜ⻝ᔷἱ⹐⃞⃘།ᙈቜᄣ೬ ц
㕂ম⏜تݗໜᢐலᔷἱ⹐ኩΌᕧᔷ⹐⃞⇩⍭ 栾ᄣࢲী㚣
ਘ௳ἱ⹐ف⃞تٲ╁ᚶ 栾ㅚتᅼላᄞ☟ᔷວዷᨤΌ цڒㅚᕥ 㖭⃞⇩⍭╁ᚶᖺㅛㅻ - * ♭ទ᪤ங 5RVHQKDLQ ⃞✖⸵⏬ⷒ᪉ߊر
܊⃞ цڒㆧ═࠶⃞ ³ᡞ᭭␡ᨷ´ 栾⸋ᕄ⎮ᕧ 1839 ၣ⃘ⲯ ц 㕂ম⇩⍭ဉۦ⃞Ḛ㦼ᖺໜسী⃞ᔷ࢛ᔆ✌☑⾨܊ цڒໜᢐ லᔷἱ⹐Όᕧ⍕࢛ἱ⹐ хᄴ࢛ᕥ⌫ἱ⹐ 栾࡚فٗউἱᖺ ڒᐋ⃞ цڒখໜᢐலᔷἱ⹐Όᕧऑࣸਘ࢛ᚬࣸ 栾ࣝ⎧٦
ັ㘢 ² 㕂মᕥ⌫⍕࢛⃞ᕟἱ⹐ цㅚتᕥᨷⶫ᧳٦ࣸਘೳᕄ
فتٲ॒࢛㊟⃞ક㙃 栾ؿ܃ᄴ࢛ᕥ⌫⃞⇩⍭ㅪࡏتݗᕟ⃞⃘།
ᗆᙛ цᄞ܊ 栾$ ࠽⥿ယڃ &OHEVFK ᔌㅪ٦㕂ম⃞ဉۦ 桍॒ၣ
ِᄞ + / ) ٸ൘㕷⣪ +HOPKROW] ጮ㕂ম⃞ࣸউἱࡑΌࢲ ت⠴Ḏἱف ц
㕂মⲟࢧἱ⹐ٜސ٦ళᆄ⃞ဉۦ ц1841 ၣࢩڒ⓼╚
⇩⍭٦ⲟࢧἱ⹐ 栾ᏰႵ٦ڜᔷⲟࢧ⃞ኩΌ 栾Ⴣ⎧٦ᔷ
ⲟࢧ ᄞ܊⍄ِ㕂মⲟࢧ 栾ؿໜ࡚ኩΌࢲᔷ┺⃞℩㓊
ᆄ х೬㊟⍕࢛⃞⻝㊡⻝ᐔਘދᄴ࢛ᕥ⌫⃞⇩⍭ف ц
ᙌ㓊ت㔝ދᄴ࢛ᕥ⌫ਘ࢛ᚬࣸ⃞ೲ࢛⇩⍭ဉۦᖺڒঔغِᄞ ڞ ³ऑࣸ⺋⚉´ 9RUOHVXQJHQ hEHU '\QDPLN 㙃⃘ⲯ⃞ 1866 ၣ ࠽⥿ယᙈ⃘ⲯ ц
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