Relevant bibliographies by topics / Hyperelliptic Integrals

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Hyperelliptic Integrals'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Hyperelliptic Integrals"

1

PAKULIAK, S., and A. PERELOMOV. "RELATIONS BETWEEN HYPERELLIPTIC INTEGRALS." Modern Physics Letters A 09, no. 19 (1994): 1791–97. http://dx.doi.org/10.1142/s0217732394001647.

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A simple property of the integrals over the hyperelliptic surfaces of arbitrary genus is observed. Namely, the derivatives of these integrals with respect to the branching points are given by the linear combination of the same integrals. We check that this property is responsible for the solution to the level zero Knizhnik-Zamolodchikov equation given in terms of hyperelliptic integrals.
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Mingari Scarpello, Giovanni, та Daniele Ritelli. "The hyperelliptic integrals and π". Journal of Number Theory 129, № 12 (2009): 3094–108. http://dx.doi.org/10.1016/j.jnt.2009.06.002.

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WANG, JIHUA, DONGMEI XIAO, and MAOAN HAN. "THE NUMBER OF ZEROS OF ABELIAN INTEGRALS FOR A PERTURBATION OF HYPERELLIPTIC HAMILTONIAN SYSTEM WITH DEGENERATED POLYCYCLE." International Journal of Bifurcation and Chaos 23, no. 03 (2013): 1350047. http://dx.doi.org/10.1142/s0218127413500478.

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In this paper, we provide a complete study of the zeros of Abelian integrals obtained by integrating the 1-form (α + βx + x2)ydx over the compact level curves of the hyperelliptic Hamiltonian [Formula: see text]. Such a family of compact level curves is bounded by a polycycle passing through a nilpotent cusp and a hyperbolic saddle of this hyperelliptic Hamiltonian system, which is not the exceptional family of ovals proposed by Gavrilov and Iliev. It is shown that the least upper bound for the number of zeros of the related hyperelliptic Abelian integral is two, and this least upper bound can
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4

Moura, Claire. "On the multiplicity of hyperelliptic integrals." Nonlinearity 17, no. 6 (2004): 2057–68. http://dx.doi.org/10.1088/0951-7715/17/6/004.

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Loiseau, Jean-Francis, Jean-Pierre Codaccioni, and R{égis Caboz. "Hyperelliptic integrals and multiple hypergeometric series." Mathematics of Computation 50, no. 182 (1988): 501. http://dx.doi.org/10.1090/s0025-5718-1988-0929548-0.

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Loiseau, J. F., J. P. Codaccioni, and R. Caboz. "Incomplete hyperelliptic integrals and hypergeometric series." Mathematics of Computation 53, no. 187 (1989): 335. http://dx.doi.org/10.1090/s0025-5718-1989-0972371-2.

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Spandaw, Jeroen, and Duco van Straten. "Hyperelliptic integrals and generalized arithmetic–geometric mean." Ramanujan Journal 28, no. 1 (2012): 61–78. http://dx.doi.org/10.1007/s11139-011-9353-7.

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Sekiguchi, J. "Systems of uniformization equations and hyperelliptic integrals." Journal of Mathematical Sciences 175, no. 1 (2011): 57–79. http://dx.doi.org/10.1007/s10958-011-0333-7.

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9

Konopelchenko, B. G., and W. K. Schief. "Integrable discretization of hodograph-type systems, hyperelliptic integrals and Whitham equations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2172 (2014): 20140514. http://dx.doi.org/10.1098/rspa.2014.0514.

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Based on the well-established theory of discrete conjugate nets in discrete differential geometry, we propose and examine discrete analogues of important objects and notions in the theory of semi-Hamiltonian systems of hydrodynamic type. In particular, we present discrete counterparts of (generalized) hodograph equations, hyperelliptic integrals and associated cycles, characteristic speeds of Whitham-type and (implicitly) the corresponding Whitham equations. By construction, the intimate relationship with integrable system theory is maintained in the discrete setting.
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Varchenko, Alexander. "Hyperelliptic integrals modulo $p$ and Cartier–Manin matrices." Pure and Applied Mathematics Quarterly 16, no. 3 (2020): 315–36. http://dx.doi.org/10.4310/pamq.2020.v16.n3.a1.

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Dissertations / Theses on the topic "Hyperelliptic Integrals"

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Cai, Yulin. "Integral Points on Modular Curves, Singular Moduli and Conductor-Discriminant Inequality." Thesis, Bordeaux, 2020. http://www.theses.fr/2020BORD0098.

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Cette thèse traite de trois sujets en trois parties. Dans la première partie, nous étudions les points S-entiers de la courbe modulaire X0(p). Yuri Bilu a montré qu’en utilisant la méthode de Baker, on peut donner une borne effective de la hauteur de ces points en fonction de p, du corps de base et de l’ensemble de places S. Min Sha a rendu ce résultat explicite. avec une borne doublement exponentielle en dans p. Nous améliorons considérablement dans cette thèse le résultat de Sha, en obtenant une borne simplement exponentielle. Cela se fait en utilisant une version très explicite du principe
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2

Fittouhi, Yasmine. "Étude des fibres singulières des systèmes de Mumford impairs et pairs." Thesis, Poitiers, 2017. http://www.theses.fr/2017POIT2252/document.

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Cette thèse est consacrée à l'étude des fibres de l'application moment du système de Mumford (pair ou impair) d'ordre g>0. Ces fibres sont paramétrées par des courbes hyperelliptiques de genre g. Comme l'a démontré Mumford, la fibre au-dessus d'une telle courbe lisse est la jacobienne de la courbe, moins son diviseur thêta. Nous décrivons les fibres au-dessus d'une courbe singulière, à la fois de manière algébrique et géométrique. Pour ce faire, nous utilisons de façon essentielle les g champs de vecteurs du système de Mumford, qui définissent une stratification de chaque fibre, où chaque s
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Books on the topic "Hyperelliptic Integrals"

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Dragović, Vladimir. Poncelet Porisms and Beyond: Integrable Billiards, Hyperelliptic Jacobians and Pencils of Quadrics. Springer Basel AG, 2011.

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2

Neue theorie der ultraelliptischen functionen. 2nd ed. Mayer & Müller, 1991.

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3

Roberts, W. R. Westropp, and R. R. Hartford. Elliptic and Hyperelliptic Integrals and Allied Theory. Cambridge University Press, 2016.

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Vorlesungen über die theorie der hyperelliptischen integrale. B. G. Teubner, 1990.

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Book chapters on the topic "Hyperelliptic Integrals"

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Holod, P., and T. Skrypnyk. "Integrable Evolutionary Equations Via Lie Algebras on Hyperelliptic Curves." In Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory. Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0670-5_12.

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"Halves of Points of an Odd Degree Hyperelliptic Curve in its Jacobian." In Integrable Systems and Algebraic Geometry. Cambridge University Press, 2020. http://dx.doi.org/10.1017/9781108773355.005.

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Nijhoff, F. W., and V. Z. Enolskii. "Integrable mappings of KdV type and hyperelliptic addition formulae." In Symmetries and Integrability of Difference Equations. Cambridge University Press, 1999. http://dx.doi.org/10.1017/cbo9780511569432.007.

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Conference papers on the topic "Hyperelliptic Integrals"

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Bertrand, Laurent. "On the implementation of a new algorithm for the computation of hyperelliptic integrals." In the international symposium. ACM Press, 1994. http://dx.doi.org/10.1145/190347.190419.

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