Raftul cu initiativa Book Archive

Mathematics

Seiu Local 36 Benefits Office: The Y2k Crisis and Its by Ira Yermish

By Ira Yermish

Show description

Read Online or Download Seiu Local 36 Benefits Office: The Y2k Crisis and Its Aftermath PDF

Best mathematics books

Measurement

For seven years, Paul Lockhart’s A Mathematician’s Lament loved a samizdat-style attractiveness within the arithmetic underground, ahead of call for caused its 2009 e-book to even wider applause and debate. An impassioned critique of K–12 arithmetic schooling, it defined how we shortchange scholars by means of introducing them to math the other way.

Control of Coupled Partial Differential Equations

This quantity comprises chosen contributions originating from the ‘Conference on optimum regulate of Coupled platforms of Partial Differential Equations’, held on the ‘Mathematisches Forschungsinstitut Oberwolfach’ in April 2005. With their articles, top scientists conceal a extensive variety of themes comparable to controllability, feedback-control, optimality platforms, model-reduction ideas, research and optimum keep an eye on of move difficulties, and fluid-structure interactions, in addition to difficulties of form and topology optimization.

Basic Hypergeometric Series, Second Edition (Encyclopedia of Mathematics and its Applications)

This up-to-date version will proceed to fulfill the wishes for an authoritative finished research of the quickly turning out to be box of simple hypergeometric sequence, or q-series. It comprises deductive proofs, workouts, and valuable appendices. 3 new chapters were extra to this variation overlaying q-series in and extra variables: linear- and bilinear-generating capabilities for simple orthogonal polynomials; and summation and transformation formulation for elliptic hypergeometric sequence.

Extra info for Seiu Local 36 Benefits Office: The Y2k Crisis and Its Aftermath

Example text

RÓ➐❒❢Ò ❷✝⑥✏⑤ ❶❈➄✡✇②①❈➄③ ❳☞③▲❺②❺②③●✑ê ❉✝✉❢Ñ ✇②⑤ ❶❈➄❛⑥ ❯⑧ ❺②⑤ ✇②③▲❺②⑤ ❒❙❶➅❻➞Ù☎Ñ⑦⑥✏❒✆✲✍⑤ ③▲❷❈Ñ ③❯Ò➠✉❢⑤ ✇♥✉❢❶✝❮❬t✈✉❢❶❈❒❙①✝✉❢❺②④❬✉➢Ó☞❷❈④ V③ ⑧ ➺ ⑩❜❶ ⑦ ✉❢❶✝❮✟ë➃⑤❧③ ➍ ✷➟ ⑦ ①✝✉➢➤❙③ ③⑨⑥r✇◆✉❢Û❈Ñ ⑤⑦⑥✏①❈③⑨❮✟✇②①❈③➃④✡❒❊❮❊❷❈Ñ⑦✉❢❺②⑤ ✇rÓ✟❒❢Ò V ❷✝⑥✏⑤ ❶❈➄❏❄ ⑤ Ñ ③⑨⑥✯④✡③❯✇②①❈❒❊❮❏❻✴è♥①❈③➃✉❢Û➭❒❭➤❙③☎×❈❺②❒☞❒❢Ò➅❒❢Ò ❳❊✉❢⑤ ✇②❒❬✉❢❶✝❮➐ë✓❷❈⑤➅⑤⑦⑥✧④✡❒❙❺②③Ú➄❙③▲❒❙④✡③❯✇②❺②⑤⑦⑧➃✉❢Ñ ❒❙❶❈➄ù✇②①❈③➪Ñ ⑤ ❶❈③➪❒❢Ò✴è➞✉❭✇②③✗✖ ⑥✧⑧❯❒❙❶✙✘r③⑨⑧●✇②❷❈❺②③❙❻ ♣✤❼ ☞ r✰❽ ➂✹✇ Ï ❻✧Ý✧③⑨⑧❯③▲❶❛✇②Ñ Ó❙❸✙❳❊⑧◆①❩❺❊✇✏✇✚③ ➜ →✝➽ ⑩❜❶ ⑦ ①✝✉❙⑥➅✉❢×❈×❈Ñ ⑤ ③⑨❮✍✇②①❈③✬⑧❯❒❙❶✝⑥r✇②❺②❷✝⑧●✇②⑤ ❒❙❶Ú❒❢✳Ò ❳❊⑧◆①❈❒☞③▲❶➃✇②❒♥✇ ✕ ⑤⑦⑥r✇②③⑨❮ ⑥✏③▲Ñ Ò€♠❽ ✔✝Û➭③▲❺➮×❈❺②❒❊❮❊❷✝⑧●✇◆⑥ ①❈③▲❺②③ ⑤⑦⑥Ú✇②①❈③➐❶✝✉❭✇②❷❊❽ ❺◆✉❢Ñ✴×❈❺②✟❒ ✘r③⑨⑧●✇②⑤ ❒❙❶➍✉❢❶✝❮ (Sπ ⑤⑦⑥➮✉ï,❶❈pr) ❒❙❶❊❽➽✇②×❺②⑤ ➤☞⑤⑦✉❢(SÑ✬✉❢❷❊✇②❒❙,④✡π❒❙◦❺②×❈pr) ①❈⑤⑦⑥✏④ ✕ ❒❢Ò P pr⑤ ❶❛✇②③▲❺◆⑧◆①✝✉❢❶❈➄❙⑤ ❶❈➄ ❻➐Ð✬①❈❒☞❒❛⑥✏⑤ ❶❈➄ ✉❢×❈×❈❺②❒❙×❈❺②⑤⑦✉❭✇②③▲Ñ Ó❙❸❏①❈③❬❒❙Û❊✇◆✉❢⑤ ❶❈③⑨❮✈Ò➹❒❙❷❈❺➪④✡❒❙❺②③✟❺②⑤ ➄❙⑤⑦❮➍Ð✯✉❢Ñ⑦✉❢Û❈⑤ ê 0, 1, ∞ ë✬✉❢❷✮✇②①❈❺②③▲③❯Ò➹❒❙Ñ⑦❮❈⑥➐❒❭➤❙③▲π❺ Q ✉❙⑥②⑥✏❒❊⑧❯⑤⑦✉❭✇②③⑨❮➊✇②❒➊⑧❯❷✝⑥✏× Ò➹❒❙❺②④❬⑥➐❒❢Ò ✕ ③▲⑤ ➄❙①❛✇ 4 ✉❢❶✝❮✮Ñ ③▲➤❙③▲Ñ ✉❢❶✝❮ ❻ ➆☎⑤⑦⑥➸④✡③❯✇②①❈❒❊❮❀⑥✏①❈❒❙❷❈Ñ⑦❮ ✕ ❒❙❃❺ ❂➈Ò➹❒❙❺➸❒❢✇②①❈③▲❺➸➄❙❺②❒❙❷❈×✝⑥➐Ñ ⑤⑦⑥r✇②③⑨❮✮⑤ ❶ 10, 17, 21 è♥①❈③▲❒❙❺②③▲④ ❾❊❻ ❼❈❻ 73 ➐ ➛ ➙ ❃➟ ➒î➛ ❺ ➜➞➑ ➺ ➔❛✜➒ ➽➞➛➅➜ ❋ • è♥①❈⑤⑦⑥❃④✡③❯✇②①❈❒❊❮ ①✝✉❙⑥ïÛ➭③▲③▲❶➣❮❊③▲➤❙③▲Ñ ❒❙×➭③⑨❮✩Û☞Ó Ð✯✉❢❶✝❮❊③▲Ñ⑦✉❙⑥▲❸➪❮❊③➍Ñ⑦✉❀ð➃⑥②⑥②✉✮✉❢❶✝➌ ❮ ⑥✍⑤ Ñ Ñ ③▲➄❛✉❙⑥ ③ ➐ ➜ ❺→➼➻⑨❢❸ ⑩❜❶ ⑦ ❸❭✉❢❶✝❮ ✕ ❒❙❃❺ ❂❊⑥❞Ò➹❒❙❺➅❒❙❶❈③❯❽î×✝✉❢❺◆✉❢④✡③❯✇②③▲❺❞Ò➠✉❢④✡⑤ Ñ ⑤ ③⑨⑥❏❒❢Ò➭Ð✯✉❢Ñ⑦✉❢Û❈⑤ ê❛ë✬✉❢❷➪⑧❯❒❙④✡×❈Ñ ③❯✇②③✓⑤ ❶❊❽ ✇②③▲❺◆⑥✏③⑨⑧●✇②⑤ ❒❙❶➐✇②①❈❺②③▲③❯Ò➹❒❙Ñ⑦❮❈⑥▲❻❫è♥①❈③Úñ✓⑤⑦⑧▲✉❢❺◆❮❛✑ê ❉❈❷✝⑧◆①✝⑥✯❮❊⑤ ❁❞③▲❺②③▲❶❛✇②⑤⑦✉❢Ñ❞✬③ ❫❛❷✝✉❭✇②⑤ ❒❙❶✝⑥✬❒❢Ò✕✇②①❈③⑨⑥✏③✍Ò➠✉❢④✡⑤ Ñ ⑤ ③⑨⑥ ✇②❷❈❺②❶ï❒❙❷❊✇✧✇②❒❬Û➭③ù➁Ú✉❢❷✝⑥②⑥✧①☞Ó☞×➭③▲❺②➄❙③▲❒❙④✡③❯✇②❺②⑤⑦⑧➃⑥✏③▲❺②⑤ ③⑨⑥▲❻✓Ù✯✇✍⑧❯❒❙❶❈⑤ Ò➹❒❙Ñ⑦❮➘×➭❒❙⑤ ❶❛✇◆⑥➮ì➹⑤➽❻ ③❙❻ ❸✝✉❙⑥②⑥✏⑤ ➄❙❶❈⑤ ❶❈➄ ⑥✏×➭③⑨⑧❯⑤⑦✉❢Ñ♥➤❭✉❢Ñ ❷❈③⑨⑥✟✇②❒✂✇②①❈③ï×✝✉❢❺◆✉❢④✡③❯✇②③▲❺●í●❸✬⑧❯③▲❺✏✇◆✉❢⑤ ❶➊❒❙❶❈③❯❽î×✝✉❢❺◆✉❢④✡③❯✇②③▲❺➮Ò➠✉❢④✡⑤ Ñ ⑤ ③⑨⑥✡➄❙⑤ ➤❙③➘❺②⑤⑦⑥✏③➸✇②❒ ❺②⑤ ➄❙⑤⑦❮❃Ð✯✉❢Ñ⑦✉❢Û❈⑤ ê❛ë✬✉❢❷➐✇②①❈❺②③▲③❯Ò➹❒❙Ñ⑦❮❈⑥▲❸✝✉❢❶✝❮➐✇②①❈③▲⑤ ❺☎④✡❒❊❮❊❷❈Ñ⑦✉❢❺②⑤ ✇rÓ➐⑧▲✉❢❶ïÛ➭③➪③⑨⑥r✇◆✉❢Û❈Ñ ⑤⑦⑥✏①❈③⑨❮➘⑥r✇②❷✝❮❊Ó☞⑤ ❶❈➄ ×➭③▲❺②⑤ ❒❊❮❈⑥♥❒❢Ò➞✇②①❈③ÚÒ➠✉❢④✡⑤ Ñ ⑤ ③⑨⑥▲❻ ↕❯➙ ✜➒ ➔❛✭➓ → ➔☞➜➞➟➠➔❊✜➒ ➔➾➽➅➔❈→❙➛✝➏❫➟➠➔ ➙ ➑ ❋ • è♥①❈⑤⑦⑥✡④✡③❯✇②①❈❒❊❮✮①✝✉❙⑥✡❶❈❒❢✇➐Ó❙③❯✇❬×❈❺②❒❊❮❊❷✝⑧❯③⑨❮✷❺②③⑨⑥✏❷❈Ñ ✇◆⑥▲❻ ⑩ ✕ ❒❙❷❈Ñ⑦❮✷Ñ ⑤ ❂❙③➘✇②❒➍④✡③▲❶❛✇②⑤ ❒❙❶➊✇②①❈⑤⑦⑥ ✉❢×❈×❈❺②❒❛✉❙⑧◆①❃①❈❒❙×❈⑤ ❶❈➄➐✇②①✝✉❭✇➪⑥✏❒❙④✡③▲❒❙❶❈③ù④✡⑤ ➄❙①❛✇ ✕ ❒❙❃❺ ❂➘❒❙❶❄⑤ ✇⑨❻➮è♥①❈③ïì➽➁➃❺②⑤ ✉✡✇②①➭íù❋€❖✝➼❨❘❯❉●❳❬❘◆➱❭❋➠❩❭➼❨❘ ❦❊❩❙❑◆➻❙ã❯❋➠❩❭❖➐❒❢Ò❫✉➐Ð✯✉❢Ñ⑦✉❢Û❈⑤ ê❛ë✬✉❢❷➸✇②①❈❺②③▲③❯Ò➹❒❙Ñ⑦❮ ⑤⑦⑥☎❮❊❑③ ✔✝❶❈③⑨❮➸Û☞Ó X Γ1 (6) J 2 (X) = P1 Γ1 (6) 1 H 1,2 (X) ⊕ H 0,3 (X) .

L (X, s) = P (p ) × ( ⑩❨❶❃×✝✉❢❺✏✇②⑤⑦⑧❯❷❈Ñ⑦✉❢❺⑨❸❊⑤ Ò i = d = ✇②①❈③ù❮❊⑤ ④✡③▲❶✝⑥✏⑤ ❒❙❶ï❒❢Ò X ❸ ✕ ③➮⑥✏⑤ ④✡×❈Ñ Ó ✕ ❺②⑤ ✇②③ L(X, s) ⑤ ❶❃×❈Ñ⑦✉❙⑧❯③ ❒❢Ò L (X, s) ✉❢❶✝❮➘⑤ ✇◆⑥✧Ñ ❒❊⑧▲✉❢Ñ❞Ò➠✉❙⑧●✇②❒❙❺♥Û☞Ó P (T ) ⑤ ❶✝⑥r✇②③⑨✉❙❮➸❒❢Ò P (T ) ❻ i et i X, i p −s −1 p= i p i −s −1 p= d p d p ❶ ♥➊➉ ➽❧➔➲→➈➛➅➜➞➝ ❺ ➔❊➓❭➟➹➒✒➓➈➛❜➒▼➔ ❺❃❺ ➟✲➼➞➒⑨➟➠→➸→❙➝✕➓ ➑ ➔☞➑➐➛ ➑ ➔❛➓ Q ☎❒ ③✍✉❙❮❈❮❊❺②③⑨⑥②⑥❫✇②①❈③✍④✡❒❊❮❊❷❈Ñ⑦✉❢❺②⑤ ✇rÓ✟❒❢Ò✕❮❊⑤ ④✡③▲❶✝⑥✏⑤ ❒❙❶ Ð✯✉❢Ñ⑦✉❢Û❈⑤ ê❛ë✬✉❢❷❬➤❭✉❢❺②⑤ ③❯✇②⑤ ③⑨⑥✓❮❊③❑✔✝❶❈③⑨❮ ❒❭➤❙③▲❺ Q✕ ❻✜✕ ❥➅③❯✇ E Û➭③✟✉❢❶✈③▲Ñ Ñ ⑤ ×❊✇②⑤⑦⑧ù⑧❯❷❈❺②➤❙③➮❒❭➤❙③▲❺ Q ❸❞✉❢❶✝❮❃1Ñ ③❯✇ ∆ ❮❊③▲❶❈❒❢✇②③ù⑤ ✇◆⑥➃❮❊⑤⑦⑥②⑧❯❺②⑤ ④✡⑤ ❶✝✉❢❶❛✇⑨❻ è♥①❈③▲❶❬⑤ ✇◆⑥ ❽❨⑥✏③▲❺②⑤ ③⑨⑥✴⑧▲✉❢❶❬Û➭③✍Û❈❷❈⑤ Ñ ✇✯❷❈×❬Û☞Ó✡⑧❯❒❙❷❈❶❛✇②⑤ ❶❈➄➪✇②①❈③☎❶☞❷❈④ùÛ➭③▲❺✬❒❢Ò F ê☞❺◆✉❭✇②⑤ ❒❙❶✝✉❢Ñ❈×➭❒❙⑤ ❶❛✇◆⑥ ❒❙❶ E ❻ L ❸ p ∞ L(E, s) = ①❈③▲❺②③ p ❺②❷❈❶✝⑥☎✉❢Ñ Ñ❏×❈❺②⑤ ④✡③⑨⑥▲❸❈✉❢❶✝❮ p ✕ 1 a(n) = −s 1−2s 1 − a(p)p + ε(p)p ns n=1 ⑤Ò p ∆ a(p) = ⑤Ò p|∆ ➁➃⑤ ➤❙③▲❶✮✉ ×❈❺②⑤ ④✡③ ❸♥③⑨✉❙⑧◆①✷Ñ ❒❊⑧▲✉❢Ñ❆❀✓❷❈Ñ ③▲❺ ❽➽Ò➠✉❙⑧●✇②❒❙❺✡❒❢Ò ⑧▲✉❢❶✮Û➭③❄❮❊③❯✇②③▲❺②④✡⑤ ❶❈③⑨❮ ③❯↔❊×❈Ñ ⑤⑦⑧❯⑤ ✇②Ñ Ó➮❷✝⑥✏⑤ ❶❈➄✍✇②①❈③✧p✉❢Û➭❒❭➤❙③✯❮❊③⑨⑥②⑧❯❺②⑤ ×❊✇②⑤ ❒❙❶➅❻❡➆☎p❒ ✕ ③▲➤❙③▲❺⑨❸⑨✇②①❈③▲L(E, ❺②③♥✉❢❺②③✯s)⑤ ❶✑✔✝❶❈⑤ ✇②③▲Ñ Ó➮④❬✉❢❶☞Ó✿❀✓❷❈Ñ ③▲❺ Ò➠✉❙⑧●✇②❒❙❺◆⑥▲❻✴Ù ❶✝✉❭✇②❷❈❺◆✉❢Ñ✌❫❛❷❈③⑨⑥r✇②⑤ ❒❙❶ï⑤⑦✱⑥ ❋ ➎◆■Ú➼➹▼❈❘❯❉②❘✟❩❭❖☛✂ù➴❢❚ ➻❙ã◆❩❭❚❛➾◆❇❊❖❞❑❯➼➽❋➠➻❭❖❄➼➹▼❈❩❭➼✧➱❙❘❯➼❨❘❯❉●❳✟❋€❖❞❘●■➪➼➹▼❈❘ ❲î■▲❘❯❉●❋➠❘●■ L L(E, s) ➏ p + 1 − #E(Fp ), ε(p) = 1 0, ±1, ε(p) = 0 ❜✇ ❿➁ q ✏✑✍❿✇✮✠✽✡✷➇❼✠✳②✹①✟②✎③✈✇ ➈ ❽ ❿② ➂❯➀➺②✎④❜✇❤✏✑✍❿✇❤✏✳✒ ❻ ②✎④ ❤✍ ➃ ♥è ①❈③✟✉❢❶✝⑥ ✕ ③▲❺✧✇②❒➐✇②①❈⑤⑦⑥✥❫❛❷❈③⑨⑥r✇②⑤ ❒❙❶✈⑧❯❒❙④✡③⑨⑥✧Ò➹❺②❒❙④ ✉❍❫❛❷❈⑤ ✇②③✟❮❊⑤ ❁❞③▲❺②③▲❶❛✇Ú⑥✏❒❙❷❈❺◆⑧❯③❙❻☎⑩❨❶✝❮❊③▲③⑨❮❏❸✝✇②①❈⑤⑦⑥ ⑤ Ñ Ñ➞✇◆✉✟❂❙③ù❷✝⑥✍✇②❒➘④✡❒❙❺②③✟✉❢❶✝✉❢Ñ Ó❛✇②⑤⑦⑧➮❒❙Û✑✘r③⑨⑧●✇◆⑥▲❻❏❳☞❒ ③ ⑤ Ñ Ñ✴❶❈❒ ❮❊③❑✔✝❶❈③✟④✡❒❊❮❊❷❈Ñ⑦✉❢❺➃➄❙❺②❒❙❷❈×✝⑥▲❸ ✕ ④✡❒❊❮❊❷❈Ñ⑦✉❢❺➮Ò➹❒❙❺②④❬⑥✟✉❢❶✝❮➈⑧❯❷✝⑥✏×➍Ò➹❒❙❺②④❬⑥▲❻✽❥➅③❯✇ H ❮❊③▲✕ ❶❈❒❢✇②✕ ③➐✇②①❈③➘❷❈✕ ×❈×➭③▲❺✏❽î①✝✉❢Ñ Ò☎⑧❯❒❙④✡×❈Ñ ③❯↔➍×❈Ñ⑦✉❢❶❈③ ✉❢❶✝❮❬Ñ ③❯✇ Û➭③✍✇②①❈③✍➄❙❺②❒❙❷❈×➐❒❢Ò ⑤ ❶❛✇②③▲➄❙❺◆✉❢Ñ✝④❬✉❭✇②❺②⑤⑦⑧❯③⑨⑥ ⑤ ✇②①➘❮❊③❯✇②③▲❺②④✡⑤ ❶✝✉❢❶❛✇ ✉❢❶✝❮ ×❈❷❊✇ P SLSL(Z)(Z)= SL (Z)/ ± I ✕ 2①❈×③▲❺②2③ I ❮❊③▲❶❈❒❢✇②③⑨⑥✯✇②①❈③➪⑤⑦❮❊③▲✕ ❶❛✇②⑤ ✇rÓ➸④❬✉❭✇②❺②⑤ ↔➸❒❢Ò❫❺◆✉❢1✳❶ ❂ 2 ❻ ↔ ➆✒↕❦➙✰➛✡➜✡➛✍➇❿➙➩➨✹➌✡➊ ♥ ❥➅③❯✇ N 1 Û➭③➮✉❢❶ï⑤ ❶❛✇②③▲➄❙③▲❺⑨❸❊✉❢❶✝❮➘Ñ ③❯✇ 2 2 Γ0 (N ) = { 2 a c 2 b d 2 ∈ P SL2 (Z) | c ≡ 0 (mod N ) } ⊂ P SL2 (Z) Û➭③➮✉✡⑧❯❒❙❶❈➄❙❺②❷❈③▲❶✝⑧❯③Ú⑥✏❷❈Û❈➄❙❺②❒❙❷❈×➘❒❢Ò P SL (Z) ❻ ❥➅③❯✇ Û➭③✈✉✂❶❈❒❙❶❊❽î❶❈③▲➄❛✉❭✇②⑤ ➤❙③➸⑤ ❶❛✇②③▲➄❙③▲❺⑨❻✮Ù ❳❬➻⑨➱❭❇❊❚ ❩❭❉➪➾❯➻❭❉●❳ f ➻r➾➘➶✬❘❯❋ ➴➢▼☞➼ k 1 ➻❭❖ k ⑦ ⑤ ☎ ⑥ ✉✡⑧❯❒❙④✡×❈Ñ ③❯↔☞❽î➤❭✉❢Ñ ❷❈③⑨❮➸①❈❒❙Ñ ❒❙④✡❒❙❺②×❈①❈⑤⑦⑧☎Ò➹❷❈❶✝⑧●✇②⑤ ❒❙❶ï❒❙❶ H ⑥②✉❭✇②⑤⑦⑥rÒ➹Ó☞⑤ ❶❈➄✟✇②①❈③ÚÒ➹❒❙Ñ Ñ ❒ ✕ ⑤ ❶❈➄ Γ (N ) ✇②❺◆✉❢❶✝⑥rÒ➹❒❙❺②④❬✉❭✇②⑤ ❒❙❶➸❺②❷❈Ñ ✗③ ❋ Ò➹❒❙❺ z ∈ H ✉❢❶✝❮ a b ∈ Γ (N ).

Az + b f( ) = (cz + d) f (z) c d cz + d Ù ❑❯❇☞■➽ø➪➾❯➻❭❉●❳ f ➻r➾♥➶✬❘❯❋ ➴➢▼☞➼ k ➻❭❖ Γ (N ) ⑤⑦⑥✓✉✍④✡❒❊❮❊❷❈Ñ⑦✉❢❺❫Ò➹❒❙❺②④➣➤❭✉❢❶❈⑤⑦⑥✏①❈⑤ ❶❈➄Ú✉❭✇✓✉❢Ñ Ñ❈⑧❯❷✝⑥✏×✝⑥ ❒❢Ò Γ (N ) ❻✴⑩❨❶ï×✝✉❢❺✏✇②⑤⑦⑧❯❷❈Ñ⑦✉❢❺⑨❸ f ①✝✉❙⑥✧❧✉ ❉❈❒❙❷❈❺②⑤ ③▲❺✧③❯↔❊×✝✉❢❶✝⑥✏⑤ ❒❙❶✂ì➠✉❭✇ ∞í●❸✝✉❢❶✝❮ ✕ ③➪⑧▲✉❢❶ ✕ ❺②⑤ ✇②③ ⑤ ✇②① q = e . f (q) = n = 1 a (n) q ✕ è♥①❈③ L❽❨⑥✏③▲❺②⑤ ③⑨⑥✬❒❢Ò✴✉✡⑧❯❷✝⑥✏×➸Ò➹❒❙❺②④ f ⑤⑦⑥✧❮❊❑③ ✔✝❶❈③⑨❮➘Û☞Ó 2 0 k 0 0 0 ∞ n f L(f, s) := 2πiz ∞ af (n) ns n=1 ❸☎❒ ③✂⑥r✇◆✉❭✇②③❄✇②①❈③✂❺②③⑨⑥✏❷❈Ñ ✇ï❒❢❏Ò ❄ ⑤ Ñ ③⑨⑥➘③❯✇❃✉❢Ñ➽❻ ①❈⑤⑦⑧◆①❀×❈❺②❒❭➤❙③⑨⑥❬✇②①❈③ ⑧❯❒❙❶✙✘r③⑨⑧●✇②❷❈❺②③✂❒❢Ò ☞①❈⑤ ④ù❷❈✕ê❺◆✉✡✕ ✉❢❶✝❮➘è➞✉❢❶❈⑤ Ó❛✉❢④❬✉ù⑤ ❶➘✇②①❈③➮✉✙✉❬❺②④❬✉❭✇②⑤ ➤❙③❙❻ ✕ ❸ ③ ➉ ❼ ⑤ ➶ ⑦ ❸✑③ ➪ ➐ ⑧ ➉ ⑩ ♠ ⑦ í❭✾✕❘❯➼ E ã◆❘➍❩❭❖ ➄✁➅❉➆✝➇❿➈✝➆✔➉➬➨✹➌❲➝ ♥ tì ❄ ⑤ Ñ ③⑨⑥➘③❯✇ï✉❢Ñ➽❻ ③ ❼ ➟ ❺ ⑤ ➶ ⑦ ✑ ❘❯❚€❚ ❋ ø❞➼➽❋➠❑➐❑❯❇❊❉●➚❭❘❬➻❭➚❭❘❯❉ Q ➐ ❍❞▼❈❘❯❖ E ❋⑦■ù❳❬➻⑨➱❭❇❊❚ ❩❭❲❉ ❜♥➼➹▼❈❩❭➼♥❋⑦■❲❜✯➼➹▼❈❘❯❉②❘✟❋⑦■✡❩➘❑❯❇☞■➽ø ➍ ❖❞❘❯➶✹➎✍➾❯➻❭❉●❳ ➻r➾➪➶✬❘❯❋ ➴➢▼☞➼ 2 = 1 + 1 ➻❭❖ Γ (N ) ■●❇✝❑◆▼ï➼➹▼❈❩❭➼ f ❋❘❜ L(E, s) = L(f, s) ➐ ➐ a(n) = a (n) ∀n ➐ ➑ù❘❯❉②❘ ❋⑦■➪➼➹▼❈❘✟❑◆➻❭❖❞➱❭❇✝❑❯➼❨➻❭❉ù➻r➾ E ➐ N ➟ ➆✔➉➡➠❿➈✔➢❒➨✹➌☛➨ ♥ è♥①❈③ù×❈❺②❒☞❒❢Ò✴❒❢✵Ò ❄ ⑤ Ñ ③⑨⑥✍③❯✇Ú✉❢Ñ➽❻✧⑤⑦⑥☎✇②❒➸⑧❯❒❙④✡×✝✉❢❺②③Ú✇②①❈③➮✇ ❒ ❽❨❮❊⑤ ④✡③▲❶✝⑥✏⑤ ❒❙❶✝✉❢Ñ ➁Ú✉❢Ñ ❒❙⑤⑦⑥✓❺②③▲×❈❺②③⑨⑥✏③▲❶❛✇◆✉❭✇②⑤ ❒❙❶✝⑥✴✉❢❺②⑤⑦⑥✏⑤ ❶❈➄➪Ò➹❺②❒❙④ E ✉❢❶✝❮ f ❻❫⑩îÒ❏✇②①❈③⑨⑥✏③☎✇ ✕ ❒ 2❽❨❮❊⑤ ✕ ④✡③▲❶✝2⑥✏⑤ ❒❙❶✝✉❢Ñ❞➁Ú✉❢Ñ ❒❙⑤⑦⑥ ❺②③▲×❈❺②③⑨⑥✏③▲❶❛✇◆✉❭✇②⑤ ❒❙❶✝⑥✴✉❢❺②③✧✬③ ❫❛❷❈⑤ ➤❭✉❢Ñ ③▲❶❛✇✬④✡❒❊❮ ì➹❒❙❺✓④✡❒❊❮ í●❸❢✇②①❈③▲❶❬✇②①❈③▲Ó✡✉❢❺②③✧✬③ ❫❛❷❈⑤ ➤❭✉❢Ñ ③▲❶❛✇⑨❸☞✉❢❶✝❮ ③⑨⑥r✇◆✉❢Û❈Ñ ⑤⑦⑥✏①➸✇②①❈✆③ ❳☞①❈⑤ ④ù❷❈❺◆✉➢ê❊è➞✉❢❶❈⑤ Ó❛✉❢④❬✉ù⑧❯❒❙3✙❶ ✘r③⑨⑧●✇②❷❈❺②③Ú⑤ ❶➘5 ✇②①❈③➮✙✉ ✉❬❺②④❬✉❭✇②⑤ ➤❙③❙❻ ❳ 0 f ❻❈➣ r✰❽ ➂✹✇ ☞ ➸❬♥➊➉ ➽❧➔➲→➈➛➅➜➞➝ ❺ ➔❊➓❭➟➹➒✒➓➈➛❜➒☎➑⑨➟ ➙ ➭➝ ❺ ➔❊➓♥➒✡➔✑➓❏➒▲➓✭➔●→➈➔ ❺→➔ K3 ➑⑨➝✕➓✭➒î➔❈→✔➔☞➑ ❸☎❒ ③ ⑤ Ñ Ñ✧✉❙❮❈❮❊❺②③⑨⑥②⑥Ú✇②①❈③➘④✡❒❊❮❊❷❈Ñ⑦✉❢❺②⑤ ✇rÓ✂❒❢Ò➃❮❊⑤ ④✡③▲❶✝⑥✏⑤ ❒❙❶ 2 Ð✯✉❢Ñ⑦✉❢Û❈⑤ ê❛ë✬✉❢❷ ➤❭✉❢❺②⑤ ③❯✇②⑤ ③⑨⑥▲❸ ❶✝✉❢④✡③▲Ñ ✕ Ó❙❸ ✕ K3 ✕ ⑥✏❷❈❺✏Ò➠✉❙⑧❯③⑨⑥▲❸❊❮❊③❑✔✝❶❈③⑨❮➘❒❭➤❙③▲❺ Q ❻ ❥➅③❯✇ Û➭③✟✉❢❶✈✉❢Ñ ➄❙③▲Û❈❺◆✉❢⑤⑦⑧ ⑥✏❷❈❺✏Ò➠✉❙⑧❯③❙❝❻ ❥➅③❯✇ N S(X) Û➭③➮✇②①❈➄③ ❸☎Ô▲❺②❒❙❶☞ê✳❳☞③▲➤❙③▲❺②⑤➅➄❙❺②❒❙❷❈× ❒❢Ò X ➄❙③▲X❶❈③▲❺◆✉❭✇②③⑨❮ïÛ☞Ó✈✉❢Ñ ➄❙③▲Û❈❺◆✉❢K3 ⑤⑦⑧➪⑧❯Ó❊⑧❯Ñ ③⑨⑥✍❒❙❶ ❻Úè♥①❈③▲❶ ⑤⑦⑥➃✉❬Ò➹❺②③▲✆③ ✔✝❶❈⑤ ✇②③▲Ñ Óï➄❙③▲❶❊❽ ③▲❺◆✉❭✇②③⑨❮➍✉❢Û➭③▲Ñ ⑤⑦✉❢❶➈➄❙❺②❒❙❷❈×➅❻❄è♥①❈③ Z❽î❺◆✉❢✳❶ ❂✂❒❢Ò NXS(X) ⑤⑦⑥✟N⑧▲✉❢S(X) Ñ Ñ ③⑨❮✂✇②①❈↔③ ➣✯❋➠❑◆❩❭❉②➱✂❖✝❇❊❳❬ã◆❘❯❉Ú❒❢Ò ✉❢❶✝❮✈❮❊③▲❶❈❒❢✇②③⑨❮❃Û☞Ó ❻ ❳☞⑤ ❶✝⑧❯③ S(X) ⊆ H (X, Z) ∩ H (X, R) ❸❞✇②①❈③ùñ✓⑤⑦⑧▲✉❢❺◆❮ ✥ X ❶☞❷❈④ùÛ➭③▲❺ ρ(X) ⑤⑦⑥❬✉❭✇❬ρ(X) ④✡❒❛⑥r✇ 20 ❻✷Ù NK3 ⑥✏❷❈❺✏Ò➠✉❙⑧❯③ ⑤⑦⑥✡✬③ ❫❛❷❈⑤ ×❈×➭③⑨❮ ⑤ ✇②①✷✇②①❈③ï×➭③▲❺✏Ò➹③⑨⑧●✇ Û➭③ ×✝✉❢⑤ ❺②⑤ ❶❈➄✈⑤ ❶✝❮❊❷✝⑧❯③⑨❮➍Û☞Ó✂✇②①❈③➸⑤ ❶❛✇②③▲❺◆⑥✏③⑨⑧●✇②⑤ ❒❙❶➍×✝✉❢⑤ ❺②⑤ ❶❈➄✝✽❻ X❥➅③❯✇ T (X) := N✕ S(X) ✇②①❈③✍❒❙❺✏✇②①❈❒❙➄❙❒❙❶✝✉❢Ñ❈⑧❯❒❙④✡×❈Ñ ③▲④✡③▲❶❛✇✯❒❢Ò N S(X) ⑤ ❶ H (X, Z) ✕ ⑤ ✇②①➐❺②③⑨⑥✏×➭③⑨⑧●✇✬✇②❒➪✇②①❈⑤⑦⑥✬×➭③▲❺✏Ò➹③⑨⑧●✇ ×✝✉❢⑤ ❺②⑤ ❶❈➄✝❻☎è♥①❈③▲❶ ⑤⑦⑥✍✉❬Ñ⑦✉❭✇✏✇②⑤⑦⑧❯③ù❒❢Ò✴❺◆✉❢✳❶ ❂ ❸❞✉❢❶✝❮ï⑤⑦⑥✍⑧▲✉❢Ñ Ñ ③⑨❮➘✇②①❈③ù➄❙❺②❒❙❷❈×❃❒❙❺ ✇②①❈③➪Ñ⑦✉❭✇✏✇②⑤⑦⑧❯③➪❒❢Ò✕✇②❺◆T✉❢(X) ❶✝⑥②⑧❯③▲❶✝❮❊③▲❶❛✇◆✉❢Ñ❏⑧❯Ó❊⑧❯Ñ ③⑨⑥♥❒❙❶ X22❻ − ρ(X) ❸☎❒ ③ ✕ ⑤ Ñ Ñ✕⑥✏⑤ ❶❈➄❙Ñ ③Ú❒❙❷❊✇☎✉✡⑥✏×➭③⑨⑧❯⑤⑦✉❢Ñ✕⑧❯Ñ⑦✉❙⑥②⑥✯❒❢Ò K3 ⑥✏❷❈❺✏Ò➠✉❙⑧❯③⑨⑥▲❻ ✕ ✕ ↔ ➆✒↕❦➙✰➛✡➜✡➛✍➇❿➙➙↕✰➌✡➊ ♥ Ù K3 ⑥✏❷❈❺✏Ò➠✉❙⑧❯③ X ⑤⑦⑥ï⑥②✉❢⑤⑦❮✮✇②❒➊Û➭③➍✉ ■●❋€❖☞➴❢❇❊❚ ❩❭❉❄ì➹❒❙❺➍❃❘ ✰❙➼➽❉②❘❯❳❬❩❭❚ í➐⑤ Ò ❻ ρ(X) = 20 ❸☎❒ ③✡⑧❯❒❙❶✝⑥✏⑤⑦❮❊③▲❺➪✉➘⑥✏⑤ ❶❈➄❙❷❈Ñ⑦✉❢❺ K3 ⑥✏❷❈❺✏Ò➠✉❙⑧❯③ X ❮❊❑③ ✔✝❶❈③⑨❮❄❒❭➤❙③▲❺ Q ❻ùè♥①❈③ L❽❨⑥✏③▲❺②⑤ ③⑨⑥✍❒❢Ò ✕✈✕ ⑦ ⑤ ✧ ⑥ ❊ ❮ ③ ❑ ✔✝❶❈③⑨❮➘Û☞Ó X ➆ 2 1,1 ⊥ H 2 (X,Z) 2 ❙➄ ❒☞❒❊❮ P (p ) ①❈③▲❺②③ï✇②①❈③❄×❈❺②❒❊❮❊❷✝⑧●✇➸❺②❷❈❶✝⑥❬❒❭➤❙③▲❺➐✉❢Ñ Ñ✍➄❙❒☞❒❊❮✷×❈❺②⑤ ④✡③⑨⑥❄ì ✕ ⑤ ✇②① (∗) ⑤ ❶✝❮❊⑤⑦⑧▲✉❭✇②③⑨⑥✡✇②①❈③✈Ò➠✉❙⑧●✇②❒❙❺ ✕ ⑧❯❒❙❺②❺②③⑨⑥✏×➭❒❙❶✝❮❊⑤ ❶❈➄ù✇②❒✡Û✝✉❙❮➸×❈❺②⑤ ④✡③⑨⑥◆í●❸✝✉❢❶✝❮ ❉❈❺②❒❙Û ¯ Q )) P (T ) = det(1 − T | H (X, ⑤⑦⑥✯✉❢❶➐⑤ ❶❛✇②③▲➄❙❺◆✉❢Ñ✝×➭❒❙Ñ Ó☞❶❈❒❙④✡⑤⑦✉❢Ñ✝❒❢Ò✕❮❊③▲➄❙❺②③▲③ 22 ✕ ①❈❒❛⑥✏③✍❺②③⑨⑧❯⑤ ×❈❺②❒❊⑧▲✉❢Ñ❈❺②❒☞❒❢✇◆⑥✓①✝✉➢➤❙③✧✇②①❈③➃✉❢Û✝⑥✏❒❙Ñ ❷❊✇②③ ➤❭✉❢Ñ ❷❈③ ❻❫è♥①❈③✍❮❊③⑨⑧❯❒❙④✡×➭❒❛⑥✏⑤ ✇②⑤ ❒❙❶✡❒❢Ò❞✇②①❈③☎Ñ⑦✉❭✇✏✇②⑤⑦⑧❯③⑨⑥ ⑤ ❶✝❮❊❷✝⑧❯③⑨⑥ ✇②①❈③➮❮❊③⑨p⑧❯❒❙④✡×➭❒❛⑥✏⑤ ✇②⑤ ❒❙❶➘❒❢Ò✕✇②①❈③ L❽❨⑥✏③▲❺②⑤ ③⑨⑥ L(X, s) ❋ H (X, Z) = N S(X) ⊕ T (X) L(X, s) = (∗) p −s −1 p: p ∗ p 2 et 2 L(X, s) = L(N S(X) ⊗ Q , s) · L(T (X) ⊗ Q , s).

Download PDF sample

Rated 4.17 of 5 – based on 41 votes