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Tuesday, August 4, 2020 | History

10 edition of Riemann surfaces, theta functions, and abelian automorphisms groups found in the catalog.

Riemann surfaces, theta functions, and abelian automorphisms groups

by Robert D. M. Accola

  • 92 Want to read
  • 19 Currently reading

Published by Springer-Verlag in Berlin, New York .
Written in English

    Subjects:
  • Riemann surfaces.,
  • Functions, Theta.,
  • Automorphisms.,
  • Abelian groups.

  • Edition Notes

    StatementRobert D. M. Accola.
    SeriesLecture notes in mathematics ; 483, Lecture notes in mathematics (Springer-Verlag) ;, 483.
    Classifications
    LC ClassificationsQA3 .L28 no. 483, QA333 .L28 no. 483
    The Physical Object
    Pagination105 p. ;
    Number of Pages105
    ID Numbers
    Open LibraryOL5201685M
    ISBN 100387073981
    LC Control Number75025928

    Riemann surfaces were first defined in Riemann’s PhD dissertation [7] where he laid down the geometric foundations of the theory of functions of one complex variable. The theory was advanced much further in Riemann’s epoch-making paper on the theory of abelian functions [8]. For every integer g≥2 we obtain the complete list of groups acting as the full automorphisms groups on hyperelliptic Riemann surfaces of genus g. Discover the world's research 17+ million members.

    one-forms on a compact Riemann surface, and (b) periods of holomorphic one-forms on an abelian variety. x1. Period relations for abelian integrals of the first kind The statements (a) and (b) in Theorem are the Riemann bilinear relations for the period integrals of differentials of the first kind on a a compact Riemann surface. On Cyclic Automorphism Groups of Riemann Surfaces and Theta Functions by Fou-Lai Lin § l. Introduction This paper rely heavily on the lecture note of Accola [1]. Let Wt be a compact Riemann surface with genus g. It is well known that the group of automorphisms G of W, is of finite order if g > 1 [11, p. ]. Furthermore.

    J. Wolper, Theta functions and automorphisms of Riemann surfaces, Thesis, Brown University, Aut X if and only if y vanishes at quarter periods f 1 ; ; f 6 such that satisfy (i) through. An integer n\geq2 is said to be a genus of a finite group G if there is a compact Riemann surface of genus n on which G acts as a group of automorphisms.


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Riemann surfaces, theta functions, and abelian automorphisms groups by Robert D. M. Accola Download PDF EPUB FB2

Riemann Surfaces, Theta Functions, and Abelian Automorphisms Groups | Prof. Robert D. Accola (auth.) | download | B–OK. Download books for free.

Find books. Riemann Surfaces, Theta Functions, and Abelian Automorphisms Groups. Authors; Robert D. Accola Search within book. Front Matter. Pages i-iii. PDF. Part I. Robert D. Accola. Pages Back Matter. Pages PDF.

About this book. Keywords. Automorphism Groups Automorphismengruppe Morphism Riemann surfaces Riemannsche Fläche.

Riemann surfaces, theta functions, and abelian automorphisms groups. Berlin ; New York: Springer-Verlag, (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: Robert D M Accola.

We had intended a more comprehensive revision, including a fuller treatment of moduli problems and theta functions. Pressure of other commitments would have substantially delayed (by years) the appearance of the book we wanted to produce.

We have chosen instead to make a few modest additions and to correct a number of errors. Theta Theta functions on Riemann Surfaces | John D. Fay (auth.) | download | B–OK. Download books for free.

Find books. Bibliography I. Accola, R. M.: Riemann surfaces, theta functions, and abelian automorphisms groups. Lecture Notes in Mathematics vol. Cite this chapter as: Accola R.D.M. () Part III. In: Riemann Surfaces, Theta Functions, and Abelian Automorphisms Riemann surfaces.

Lecture Notes in Mathematics, vol   Cite this chapter as: Accola R.D.M. () Part II. In: Riemann Surfaces, Theta Functions, and Abelian Automorphisms Groups.

Lecture Notes in Mathematics, vol Riemann Surfaces and Theta Functions MAST G / MAST J M. Bertolaz1 zDepartment of Mathematics and Statistics, Concordia University de Maisonneuve W., Montr eal, Qu ebec, Canada H3G 1M8 [email protected] Compiled: Aug conveniently in terms of divisors.

In general a divisor on a Riemann surface M is a mapping d: M!Zsuch that d(p) 6= 0 only at a discrete set of points p2M; that set of points is called the support of the divisor, and is denoted by jdj.

The set of all divisors on Mclearly form an abelian group under pointwise addition of functions. It is gratifying to learn that there is new life in an old field that has been at the center of one's existence for over a quarter of a century.

It is particularly pleasing that the subject of Riemann surfaces has attracted the attention of a new generation of mathematicians from (newly) adjacent fields (for example, those interested in hyperbolic manifolds and iterations of rational maps) and 5/5(1).

that the quotient surface X/ is the Riemann sphere. The group is called the trigonality auto-morphism group. This group is unique whenever X has genus g 5, as shown by Accola in [1].

Our main result is Theoremwhere we give the list of groups acting as a group of automorphisms of a cyclic trigonal Riemann surface of genus g 5 and. Study 79 contains a collection of papers presented at the Conference on Discontinuous Groups and Ricmann Surfaces at the University of Maryland, MayThe papers, by leading authorities, deal mainly with Fuchsian and Kleinian groups, Teichmüller spaces, Jacobian varieties, and quasiconformal mappings.

These topics are intertwined, representing a common meeting of algebra. Complex Analysis 2: Riemann Surfaces, Several Complex Variables, Abelian Functions, Higher Modular Functions Eberhard Freitag (auth.) The book provides a complete presentation of complex analysis, starting with the theory of Riemann surfaces, including uniformization theory and a detailed treatment of the theory of compact Riemann surfaces, the.

Accola, R. M.: Riemann surfaces, theta functions, and abelian automorphism groups. Lecture Notes in MathematicsSpringer-Verlag, Berlin-Heidelberg-New York ().

CrossRef zbMATH Google Scholar. Holomorphic maps of Riemann surfaces and Weierstrass points Tanabe, Masaharu, Kodai Mathematical Journal, ; Non-hyperelliptic Riemann surfaces Hamilton, Richard S., Journal of Differential Geometry, ; The congruence subgroup property for the hyperelliptic modular group: the open surface case Boggi, Marco, Hiroshima Mathematical Journal.

Riemann Surfaces.- 4. Markings of Riemann Surfaces and Characteristic Classes of Factors of Automorphy.- 5. Abelian Differentials and the Jacobi Variety of a Riemann Surface.- 6. Meromorphic Abelian Differentials and the Prime Function of a Riemann Surface.- III. Generalized Theta Functions.- 7.

Theta Factors of Automorphy and Generalized Theta. On the other hand; theta functions, the action of the Heisenberg group, and the action of the modular group were obtained from the geometric quantization of the Jacobian variety, cf. This paper is about the theory of Riemann’s theta functions and its place within abelian Chern–Simons theory, as described by Witten in.

Abelian Differentials and the Jacobi Variety of a Riemann Surface.- 6. Meromorphic Abelian Differentials and the Prime Function of a Riemann Surface.- III. Generalized Theta Functions.- 7.

Theta Factors of Automorphy and Generalized Theta Functions.- 8. Generalized Theta Functions and Canonical Subvarieties of the Jacobi Variety.- 9.

II II U~IUII II II UlIII II MII III Riemann Surfaces, Theta Functions, and Abelian Automorphisms Groups m Springer-Verlag Berlin.

Heidelberg. NewYork Author Prof. Robert D. Accola Department of Mathematics Brown University Providence, R.I. USA Library of Congress Cataloging in Publication Data. The investigation of the relationships between compact Riemann surfaces (al­ gebraic curves) and their associated complex tori (Jacobi varieties) has long been basic to the study both of Riemann surfaces and of complex tori.

A Riemann surface is naturally imbedded as an analytic.V Automorphisms of Compact Surfaces-Elementary Theory.- V.l. Hurwitz's Theorem.- V Representations of the Automorphism Group on Spaces of Differentials.- V Representation of Aut M on H1(M).- V The Exceptional Riemann Surfaces.- VI Theta Functions.- VI.

1. The Riemann Theta Function.- VI The Theta Functions Associated with a Riemann. the Riemann surfaces form a closed one-dimensional equisymmetric family F ¯ g of Riemann surfaces S with a group of automorphisms G isomorphic to C g − 1 ⋊ 6 C 6 = 〈 a, c: a g − 1 = c 6 = 1, c a c − 1 = a m 〉, where m is a primitive 6-th root of unity in the field of g − 1 elements, and G acts with signature (0; 2, 2, 3, 3).