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Wednesday, July 22, 2020 | History

5 edition of On the reduction of the hyperelliptic integrals (p=3) to elliptic integrals by transformation of the second and third degrees ... found in the catalog.

On the reduction of the hyperelliptic integrals (p=3) to elliptic integrals by transformation of the second and third degrees ...

by William Gillespie

  • 101 Want to read
  • 2 Currently reading

Published by Printed by L. Hofer in Göttingen .
Written in English

    Subjects:
  • Integrals, Hyperelliptic

  • Classifications
    LC ClassificationsQA345 .G43
    The Physical Object
    Pagination40 p., 1 l.
    Number of Pages40
    ID Numbers
    Open LibraryOL6945902M
    LC Control Number04026587

    Reduction of a type of hyperelliptic integrals to elliptic integrals. Ask Question Asked 2 years, 2 months ago. Active 2 years, 2 months ago. Viewed 63 times 1 $\begingroup$ In [1] (refered to as "the handbook"), it is said that On the reduction of hyperelliptic integrals to elliptic integrals., Borchardt J. LXXXV, (). ZBL In integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals. Originally, they arose in connection with the problem of finding the arc length of an ellipse and were first studied by Giulio Fagnano and Leonhard Euler (c. ).Modern mathematics defines an "elliptic integral" as any function f which can be expressed in the form.

    Functional Analysis Elliptic Integral Moser System Hyperelliptic Integral These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves. Reduction of Algebraic Integrands to Jacobian Elliptic Functions. Paul F. Byrd, Morris D. Friedman Hyperelliptic Integrals. Paul F. Byrd, Morris D. Friedman. Pages elliptic functions and elliptic integrals. The numerous books written on elliptic integrals, while of great value to the student or mathematician, are not especially.

    a On the form of hyperelliptic integrals of the first order which are expressible as the. b On the application of Abels theorem to elliptic integrals of the first kind. a On the reduction of a linear substitution to its canonical form. used to determine all the S-integral points on the curve. 2. In the case the curve has genus 2 and the polynomial defining the curve has real roots only, we reduce the upper bound for the size of the integral points to manageable proportions using linear forms in hyperelliptic logarithms. We then find all of the integral points on Cby a.


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On the reduction of the hyperelliptic integrals (p=3) to elliptic integrals by transformation of the second and third degrees .. by William Gillespie Download PDF EPUB FB2

On the Reduction of the Hyperelliptic I [Author] on *FREE* shipping on qualifying offers. On the reduction of the hyperelliptic integrals (p=3) to elliptic integrals by transformation of the second and third degrees.

Göttingen, Printed by L. Hofer, (OCoLC) Material Type: Biography, Thesis/dissertation: Document Type: Book: All Authors / Contributors: William Gillespie. On the Reduction of Hyperelliptic Integrals (p =3) to Eltiptic Integrals by Transformations of the Second and Third Degrees.

BY WILLIAM GILESPIE. INTRODUCTION. The principal subject of this -paper is an application of cubic involution to the problem of the reduction to elliptic integrals, of hyperelliptic integrals of.

On the Reduction of Hyperelliptic Functions (p=2) to Elliptic "Functions by a Transformation of the Second Degree. A Dissertation Submitted to the Faculties of the Graduate Schools of Arts, Literature, and Science, in candidacy for the degree of IDoctor of P*liilosopliy (Department of Mathematics) by J.

JACOBI'S transformation theory of elliptic integrals and the reduction theory of hyperelliptic integrals, which is such that the latter appears as a generalization of the former. A fundamental memoir by M. PICARD 1I contains new results and suggests new problems.

It is shown that when, to the relation y2 = R6 (x), R6 (x). AND THE REDUCTION OF HYPERELLIPTIC INTEGRALS OF GENUS TWO TO ELLIPTIC INTEGRALS BY A TRANSFORMATION OF THE FOURTH ORDER* BY JOHN HECTOR McDONALD Introduction.

If a hyperelliptic integral of genus 2 is reducible to an elliptic integral by a transformation of order k then there always exists a second integral f with the. This book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula.

The hypoelliptic Laplacian is a family of operators that is supposed to interpolate between the ordinary Laplacian and the geodesic flow. The hyperelliptic integrals and p G. Mingari Scarpello and D. Ritelli Other suggestive and well-known p/2 expressions can be: p 2 2F1 1 2; 1 2;1,k2 =K(k) (5) p 2 2F1 1 2; 1 2;1,k2 =E(k) (6) where K(k) and E(k) are respectively the first and second kind complete elliptic integral of module 0.

• IBP relations from the calculus of hyperelliptic curves Based on Mads Sogaard and YZ, Alessandro Georgoudis and YZ, xxxxx For a D-dimensional L-loop Feynman integral, (1) with DL 1 propagates and (2) with smooth unitarity cut, the “on-shell” parts of IBPs correspond to exact meromorphic one-forms on an algebraic curve.

In their exceedingly interesting book Theorie des Fonctions algébriques et de leurs Intégrales, pp.Appell and Goursat have given a brief sketch of Hermite's method for obtaining by rational operations the reduced form for a hyperelliptic integral, prefacing the same by a remark which would.

This will be accomplished by reducing some hyperelliptic integrals to elliptic through the methods Legendre taught in his treatise. The complete elliptic integrals of first kind have complementary moduli: as a consequence we can find their ratio through the Lauricella F D (3) functions. In such a way we succeed in obtaining, through the theory of elliptic singular moduli, some.

On the multiplicity of hyperelliptic integrals consider ω = n i=1 c iω i, c i ∈ multiplicity of I(t)at t = t 0 is the order of contact at t = t 0 of the curve γ(t)and the linear hyperplane { n i=1 c ix i = 0}⊆C n whose coefficients are prescribed by the decomposition of ω.

Recall that γ is a solution of the Picard–Fuchs system, completely described by Novikov and. Read "New Demonstration of the Reduction of Hyperelliptic Integrals to the Normal Form., Journal für die reine und angewandte Mathematik (Crelle's Journal)" on DeepDyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips.

On the reduction of hyperelliptic functions (p=2) to elliptic functions. Göttingen, Druck der Dieterich'schen univ.-buchdruckerei (W.F. Kaestner) (OCoLC) Material Type: Biography, Thesis/dissertation: Document Type: Book: All Authors / Contributors: John Irwin Hutchinson.

Based upon a Roberts's reduction approach of hyperelliptic integrals to elliptic ones and on the simultaneous multivariable hypergeometric series evaluation of them, several identities have been. You can write a book review and share your experiences. Other readers will always be interested in your opinion of the books you've read.

Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. π and the integrals: The literary background and our aim This paper originates from the need, common to pure and applied mathematics, to compute hyperelliptic integrals in a simple fashion, avoiding Riemann two-variable Theta functions.

In both fields the Exton book [10, pages –] and some papers of the cosmologist Kraniotis [16]. On the reduction of hyperelliptic integrals to elliptic integrals., Borchardt J. LXXXV, (). ZBL aic-geometry -theory real-analysis special-functions elliptic-integrals.

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): ω be an Abelian integral, where H = δ(t) y2 −xn+1 +P(x) is a hyperelliptic polynomial of Morse type, δ(t) a horizontal family of cycles in the curves {H = t}, and ω a polynomial 1-form in the variables x and y.

We provide an upper bound on the multiplicity of I(t), away from the critical values of H. Namely: ord. The text treats such topics as the topological properties of curves, the Riemann-Roch theorem, and all aspects of a wide variety of curves including real, covariant, polar, containing series of a given sort, elliptic, hyperelliptic, polygonal, reducible, rational, the pencil, two-parameter nets, the Laguerre net, and nonlinear systems of curves.

5. Hyperelliptic curve of genus two 16 Characteristics in genus two 16 Inversion of a holomorphic integral 17 6. Hyperelliptic curve of genus three 18 Characteristics in genus three 18 Inversion of a holomorphic integral 19 7. An application: 9-dimensional Reissner-Nordstr¨om-de Sitter space-time 21 8.

Conclusion   By covering a bad reduction hyperelliptic curve by annuli and basic wide open sets, we reduce the computation of Berkovich-Coleman integrals to the known algorithms on good reduction hyperelliptic curves. These are due to Balakrishnan, Bradshaw, and Kedlaya, and to Balakrishnan and Besser for regular and meromorphic 1-forms on good reduction.

integral reduction is extremely fast, whic h has the time order of minutes. W e have the following remarks, • Although the mathematic ob jects are elliptic or hyperelliptic, we do not need the.