Results 11 to 20 of about 216 (184)
Hyperelliptic curves and newform coefficients [PDF]
Journal of Number Theory, 2021 We study which integers are admissible as Fourier coefficients of even integer weight newforms. In the specific case of the tau-function, we show that for all odd primes $\ell < 100$ and all integers $m \geq 1$, we have $$ τ(n) \neq \pm \ell, \pm 5^m.
Spencer Dembner, Vanshika Jain
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Hyperelliptic Curves with Extra Involutions [PDF]
LMS Journal of Computation and Mathematics, 2005 AbstractThe purpose of this paper is to study hyperelliptic curves with extra involutions. The locusLgof such genus-ghyperelliptic curves is ag-dimensional subvariety of the moduli space of hyperelliptic curvesHg. The authors present a birational parameterization ofLgvia dihedral invariants, and show how these invariants can be used to determine the ...
Jaime Gutierrez 0001, Tony Shaska
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Hitchin Systems on Hyperelliptic Curves [PDF]
Proceedings of the Steklov Institute of Mathematics, 2020 16 pages, 5 ...
Borisova, P. I., Sheinman, O. K.
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The a-Number of Certain Hyperelliptic Curves
Iranian Journal of Science and Technology, Transactions A: Science, 2022 9 ...
Nourozi, Vahid +2 more
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Self-pairings on hyperelliptic curves [PDF]
Journal of Mathematical Cryptology, 2013 Abstract. A self-pairing is a pairing computation where both inputs are the same group element. Self-pairings are used in some cryptographic schemes and protocols. In this paper, we show how to compute the Tate–Lichtenbaum pairing on a curve more efficiently than the ...
Steven D. Galbraith, Chang-An Zhao
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Hyperelliptic curves with many automorphisms [PDF]
International Journal of Number Theory, 2021 A complex algebraic curve is said to have many automorphisms if it cannot be deformed nontrivially together with its automorphism group. Oort asked whether the jacobian of any such curve has complex multiplication. We answer this question completely when the curve is hyperelliptic.
Müller, Nicolas, Pink, Richard
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Limits of the trivial bundle on a curve [PDF]
Épijournal de Géométrie Algébrique, 2018 We attempt to describe the rank 2 vector bundles on a curve C which are specializations of the trivial bundle. We get a complete classifications when C is Brill-Noether generic, or when it is hyperelliptic; in both cases all limit vector bundles are ...
Arnaud Beauville
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Pointless hyperelliptic curves
Finite Fields and Their Applications, 2013 In this paper we consider the question of whether there exists a hyperelliptic curve of genus $g$ which is defined over $\FF_q$ but has no rational points over $\FF_q$ for various pairs $(g,q)$.
Ryan Becker, Darren B. Glass
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An Optimal Authentication Scheme through Dual Signature for the Internet of Medical Things
Future Internet, 2023 The Internet of Medical Things (IoMT) overcomes the flaws in the traditional healthcare system by enabling remote administration, more effective use of resources, and the mobility of medical devices to fulfil the patient’s needs. The IoMT makes it simple
Zainab Jamroz +6 more
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A Note on Hyperelliptic Curves [PDF]
Proceedings of the American Mathematical Society, 1992 If \(C\) is a Riemann surface of genus one or hyperelliptic Riemann surface of genus \(\geq 2\), then \(C\) admits a map \(p: C\to P^ 1\) of degree 2 branched over \(2g+2\) points. \(p\) is unique up to action of \(PGL_ 2(C)\) on \(P^ 1\), and translation of \(C\) if genus\((C)=1\).
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