Электронная библиотека Попечительского советамеханико-математического факультета Московского государственного университета
 Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум Авторизация Поиск по указателям     Bliss G.A. — Algebraic Functions Обсудите книгу на научном форуме Нашли опечатку?Выделите ее мышкой и нажмите Ctrl+Enter Название: Algebraic Functions Автор: Bliss G.A. Аннотация: This text surveys approaches and basic results of all three classes of algebraic functions: transcendental (function theoretic), algebraic-geometric, and arithmetic. Worked examples include both exercises and explanations of methods Язык: Рубрика: Математика/ Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2004 Количество страниц: 240 Добавлена в каталог: 03.04.2008 Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID Предметный указатель
 Abel      iii iv 94 119 Abelian integrals, classification of      64 95 Abelian integrals, definition      64 93 Abelian integrals, for algebraic equations of the third degree in y      208ff (see also Elementary integrals) Abelian integrals, for elliptic and hyperelliptic curves      191ff Abelian integrals, inversion of      169ff Abelian integrals, normal integrals      110 Abelian integrals, periods      96ff 105 Abelian integrals, singularities      94 Abel’s theorem      119ff Abel’s Theorem, elementary applications of      121 Abel’s Theorem, for elementary integrals      129 Abel’s Theorem, for integrals of the first kind      116 Adjoined polynomials      153 Algebraic function, branch of      32 Algebraic function, continuations of      25 Algebraic function, defined by equation of the third or fourth degree in y      194ff Algebraic function, definition of      24 Algebraic function, discriminant      24 Algebraic function, expansions      29 35 Algebraic function, genus of      58 90 147 Algebraic function, having genus or 139 Algebraic function, hyperelliptic and elliptic cases      141 143 Algebraic function, integral algebraic function      195 Analytic functions      1 Arcs, regular      2 Arcs, regular arc on a Riemann surface      80 Arcs, simply closed      2 Barnum      123 Bases, complementary bases      59ff 200 Bases, for a divisor      48 Bases, for all rational functions      46 Bases, for special examples      196ff Bases, for the divisor and an equation of the third degree in y      196ff Bases, normal at 52 Bases, normal for the divisor and an equation of the third degree in y      202 Bases, transformation of      51 Bauer      v 197 211 213 Bauer, his methods for equations of the third degree in y      194ff Bauer, theorem of      204 Birational transformations      133ff Birational transformations, for curves of the third degree in y      203 Birational transformations, in the function- theoretic plane      167 Birational transformations, projective      144 Birational transformations, reducing singularities to double points in the projective plane      163 Birational transformations, reducing singularities to multiple points with distinct tangents      156 Branch cycle      32 56 Branch cycle, in the function-theoretic plane      166 Branch cycle, linear branch in the projective plane      160 Branch cycle, of a rational function      63 Branch cycle, primitive branch      32 159 166 Branch of an algebraic function      32 Brill      iii Canonical system of cuts      90 Canonical system of cuts, for elliptic or hyperelliptic curves      190 Cauchy      iv 2 7 84 Cauchy’s integral formula      8 Cauchy’s Theorem      3 Cauchy’s theorem, consequences of      5 7 Cauchy’s theorem, on a Riemann surface      84 92 Clebsch      iii Column order of a rational function at 52 Complementary bases      59ff 200 Connected regions      5 26 Connectivity of surfaces      82 87 Connectivity of surfaces, of a closed surface      88 Connectivity of surfaces, of a Riemann surface      86ff Continuations for an algebraic function      25 Cremona      iv 156 Cremona transformations      133 Cremona transformations, reducing singularities to multiple points with dis-tinct tangents      156 Curves, in the function-theoretic plane with double points only      165 Curves, in the projective plane with double points only      159 Curves, of elliptic and hyperelliptic types      189 Curves, of genus not greater than 2      139 Curves, of the fourth degree in x and y      210 Curves, of the third degree in y      194ff Cusps      41 Cuts      82 Cuts, canonical systems      90 Cuts, cross and loop cuts      82 Cycles for an algebraic function      32 Cycles for an algebraic function, branch cycles      56 Dedekind      iii iv Determinant 48 Discriminant of a polynomial      18 Divisor      47 Divisor, basis for a divisor      48 Divisor, ideal norm of      55 Divisor, multiples of      51 54 Divisor, of a rational function      62 Divisor, of branch cycles      56 63 Divisor, order of a divisor      62 Divisor, special divisor      71 Elementary integrals      64 102 Elementary integrals, for curves of elliptic or hyperelliptic types      191-2 Elementary integrals, for equations of the third degree in y      205 209 Elementary integrals, of first kind      65 98 151 Elementary integrals, of second kind      66 102 Elementary integrals, of third kind      66 102 Elementary integrals, period relations      106 Elliptic curves      139 Elliptic functions, analogies with rational functions on a Riemann surface      174ff Elliptic functions, further properties      177 Elliptic integrals      94 Elliptic integrals, addition formulas      123 examples      183ff Examples, algebraic functions defined by equations of the third or fourth degree in y      194ff 211 213 Examples, elliptic and hyperelliptic curves      189 Examples, for expansions      183 Examples, for Riemann surfaces      186 Expansion theorems      17 25 29 32 Expansion theorems, at singular points of special types      40 Expansion theorems, Laurent expansion      9 Expansion theorems, Newton’s polygon method      35 Fields      iii Function-theoretic plane      165 Functions, algebraic      24 Functions, analytic      1 Functions, holomorphic on a plane      1 Functions, inverse      171ff Functions, on a Riemann surface      80 Functions, rational      12ff 43ff 70 Functions, special rational      71 Fundamental systems of integrals, construction of      107 Fundamental systems of integrals, for curves of elliptic or hyperelliptic type      193-4 Fundamental systems of integrals, of the first and second kinds      103 Fundamental systems of integrals, of the first kind      98 Fundamental theorem of algebra      15 Genus, invariant property      62 Genus, of a Riemann surface      88 Genus, of an algebraic function      58 90 147 Genus, of an equation of the third degree in y      207 Genus, of elliptic or hyperelliptic curves      191 Gordan      iii Halphen      155 Hensel      iii iv v 156 Holomorphic functions, on a Riemann surface      80 Holomorphic functions, on a z-plane      1 Holomorphic functions, together forming an algebraic function      28 Hyperelliptic curves      139 189 Ideal norm of a divisor      55 Integral algebraic function      195 Integrals, associated with an algebraic function      64 93 Elliptic Integrals, of a function f(z)      2 Inverse function, when 171 Inverse function, when 172 Inversion of Abelian integrals      169ff Irreducible algebraic equations      78 jacobi      176 Klein      155 kronecker      iii v 155-6 Landsberg      iii iv v 156 Laurent expansion      9 Laurent expansion, principal part of      13 15 Leading coefficients of a rational function      74 Logarithm of a rational function      114 Multiple points with distinct tangents      40 Multiples of a divisor      47 48 51 54 72 Newton      35 Newton’s polygons      36 Noether      iii 155 Noether, Emmy      iii Norm, ideal norm of a divisor      55 Norm, of a rational function      44 Normal basis for a divisor      52 Normal form of equation of third degree in y      194 Normal integrals      110 Ordinary point      9 11 Ordinary point, ordinary place      80 Periods, of an Abelian integral      96ff 101 Periods, period relations      100 105-6 Periods, primitive periods of an elliptic function      179 Picard      155 Place on a Riemann surface      34 77 Place on a Riemann surface, for an equation of the third degree in y      207 Place on a Riemann surface, singular places      80 Place on a Riemann surface, special set of places      71 Primitive branch      32 Principal parts      15 Projective intersections of two curves      150 Projective plane      159 Projective transformations      144ff Rational function, analogies with elliptic functions      174ff Rational function, conjugate values      44 Rational function, expressed in terms of integrals      113 Rational function, in the plane      12ff Rational function, integral rational function      196 Rational function, on a Riemann surface      43ff Rational function, special rational function      71 73 Rational function, with prescribed poles      14-15 70 72 Reducibility of polynomials      21ff Reduction of singularities      155ff Reduction of singularities, to double points in the function-theoretic plane      167 Reduction of singularities, to double points in the projective plane      163 Reduction of singularities, to multiple points with distinct tangents      156 references      23 42 74 92 118 132 154 168 182 213 214 Region      26 Region, connected      5 Region, simply connected      5 26 Regular arc      2 Regular arc, on a Riemann surface      80 Residues      7 12 44 Residues, of a function on a Riemann surface      81 Residues, theorems concerning      8 11 14 45 Resultant of two polynomials      18 Riemann      iii iv 67 75 Riemann surface T      75ff Riemann surface T, construction of T, T’, and T’’      75 92 96 Riemann surface T, examples      186ff Riemann surface T, for an irreducible algebraic equation      78 Riemann surface T, genus of      88 147 Riemann surface T, places on      77 Riemann — Roch theorem      67ff Roch      iv 67 Severi      iii Simart      155 Singular places, of Abelian integrals      94 Singular places, of an algebraic function      34 Singular places, of functions on a Riemann surface      80 Singular points      9 11 Singular points, for an algebraic function      25 Singular points, of special types      40 Singularities, reduction of      155ff (see also Reduction of singularities) Special places and rational functions      71 73 Special places and rational functions, special divisor      71 Surface, connected or simply connected      82 Surface, connectivity      87 Trace of a rational function      44 Transformations, projective      144ff (see also Birational transformations Cremona Unicursal curves      139ff Weber      iii iv Weierstrass      iii 176-7 Реклама     © Электронная библиотека попечительского совета мехмата МГУ, 2004-2020 | | О проекте