Results 21 to 30 of about 216 (184)
Frontiers in Physics, 2023 In this work, we present two finite-dimensional Lie–Poisson Hamiltonian systems associated with the Hirota–Satsuma modified Boussinesq equation by using the nonlinearization method. Moreover, the separation of variables on the common level set of Casimir
Xue Geng, Dianlou Du, Xianguo Geng
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On the Discriminant of a Hyperelliptic Curve [PDF]
Transactions of the American Mathematical Society, 1994 The minimal discriminant of a hyperelliptic curve is defined and used to generalize much of the arithmetic theory of elliptic curves. Over number fields this leads to a higher genus version of Szpiro’s Conjecture. Analytically, the discriminant is shown to be related to Siegel modular forms of higher degree.
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Finite Groups for the Kummer Surface: The Genetic Code and a Quantum Gravity Analogy
Quantum Reports, 2021 The Kummer surface was constructed in 1864. It corresponds to the desingularization of the quotient of a 4-torus by 16 complex double points. Kummer surface is known to play a role in some models of quantum gravity.
Michel Planat +5 more
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The a-Number of Hyperelliptic Curves [PDF]
, 2018 It is known that for a smooth hyperelliptic curve to have a large $a$-number, the genus must be small relative to the characteristic of the field, $p>0$, over which the curve is defined. It was proven by Elkin that for a genus $g$ hyperelliptic curve $C$ to have $a_C=g-1$, the genus is bounded by ...
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On Addition Formulae for Sigma Functions of Telescopic Curves
Symmetry, Integrability and Geometry: Methods and Applications, 2013 A telescopic curve is a certain algebraic curve defined by m−1 equations in the affine space of dimension m, which can be a hyperelliptic curve and an (n,s) curve as a special case.
Takanori Ayano, Atsushi Nakayashiki
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The monodromy problem for hyperelliptic curves
Bulletin des Sciences Mathématiques, 2021 27 pages, 11 ...
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From topological recursion to wave functions and PDEs quantizing hyperelliptic curves
Forum of Mathematics, Sigma, 2023 Starting from loop equations, we prove that the wave functions constructed from topological recursion on families of degree $2$ spectral curves with a global involution satisfy a system of partial differential equations, whose equations can be ...
Bertrand Eynard, Elba Garcia-Failde
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COMPUTATIONAL ASPECTS OF HYPERELLIPTIC CURVES [PDF]
Computer Mathematics, 2003 We introduce a new approach of computing the automorphism group and the field of moduli of points $\p=[C]$ in the moduli space of hyperelliptic curves $\H_g$. Further, we show that for every moduli point $\p \in \H_g(L)$ such that the reduced automorphism group of $\p$ has at least two involutions, there exists a representative $C$ of the isomorphism ...
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Mayfly optimistic hyperelliptic curve cryptosystem
Frontiers in Computer ScienceVarious applications use asymmetric cryptography to secure communications between both parties, and it raises the main issue of generating vast amounts of computation and storage.
Ramireddy Nava Teja Reddy +7 more
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Journal of Sensor and Actuator Networks, 2023 As an extension of the wired network, the use of the wireless communication network has considerably boosted users’ productivity at work and in their daily lives.
Tahir Ali Shah +4 more
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