scholarly journals Poisson type phenomena for points on hyperelliptic curves modulo $p$

2012 ◽  
Vol 47 (1) ◽  
pp. 65-78 ◽  
Author(s):  
Kit-Ho Mak ◽  
Alexandru Zaharescu
Keyword(s):  
Hyperelliptic Curves ◽  
Modulo P ◽  
Poisson Type

scholarly journals Twists of hyperelliptic curves by integers in progressions modulo $p$

2020 ◽  
Vol 192 (1) ◽  
pp. 63-71
Author(s):  
David Krumm ◽  
Paul Pollack
Keyword(s):  
Hyperelliptic Curves ◽  
Modulo P

FORMAL GROUPS OF JACOBIAN VARIETIES OF HYPERELLIPTIC CURVES

2010 ◽  
Vol 06 (07) ◽  
pp. 1701-1716
Author(s):  
FUMIO SAIRAIJI
Keyword(s):  
Elliptic Curves ◽  
Characteristic Zero ◽  
Hyperelliptic Curve ◽  
Hyperelliptic Curves ◽  
Formal Groups ◽  
Jacobian Varieties ◽  
Explicit Constructions ◽  
Modulo P

Let k be a field of characteristic zero. In this paper, we discuss two explicit constructions of the formal groups Ĵ of the Jacobian varieties J of hyperelliptic curves C over k. Our results are generalizations of the classical constructions of formal groups of elliptic curves. As an application of our results, we may decide the type of bad reduction of J modulo p when C is a hyperelliptic curve over ℚ.

Dynamic Monopoly Pricing Under a Poisson-Type Uncertain Demand

1992 ◽  
Vol 65 (4) ◽  
pp. 593 ◽  
Author(s):  
Yu-Min Chen ◽  
Dipak C. Jain
Keyword(s):  
Uncertain Demand ◽  
Monopoly Pricing ◽  
Dynamic Monopoly ◽  
Poisson Type

scholarly journals Coleman integration for even-degree models of hyperelliptic curves

2015 ◽  
Vol 18 (1) ◽  
pp. 258-265 ◽  
Author(s):  
Jennifer S. Balakrishnan
Keyword(s):  
Number Theory ◽  
Computer Science ◽  
Hyperelliptic Curves ◽  
Open Book ◽  
Line Integral ◽  
Book Series ◽  
Numerical Examples ◽  
Lecture Notes ◽  
Integration Algorithms ◽  
Mathematical Sciences

The Coleman integral is a $p$-adic line integral that encapsulates various quantities of number theoretic interest. Building on the work of Harrison [J. Symbolic Comput. 47 (2012) no. 1, 89–101], we extend the Coleman integration algorithms in Balakrishnan et al. [Algorithmic number theory, Lecture Notes in Computer Science 6197 (Springer, 2010) 16–31] and Balakrishnan [ANTS-X: Proceedings of the Tenth Algorithmic Number Theory Symposium, Open Book Series 1 (Mathematical Sciences Publishers, 2013) 41–61] to even-degree models of hyperelliptic curves. We illustrate our methods with numerical examples computed in Sage.

scholarly journals Integral points on hyperelliptic curves

2008 ◽  
Vol 2 (8) ◽  
pp. 859-885 ◽  
Author(s):  
Yann Bugeaud ◽  
Maurice Mignotte ◽  
Samir Siksek ◽  
Michael Stoll ◽  
Szabolcs Tengely
Keyword(s):  
Hyperelliptic Curves ◽  
Integral Points

Interspike interval dependency from arterial chemoreceptors

1985 ◽  
Vol 59 (5) ◽  
pp. 1566-1570 ◽  
Author(s):  
D. F. Donnelly ◽  
W. F. Nolan ◽  
E. J. Smith ◽  
R. E. Dutton
Keyword(s):  
Carotid Body ◽  
Interspike Interval ◽  
Correlation Coefficients ◽  
Feedback System ◽  
Serial Dependence ◽  
Control Series ◽  
First Order ◽  
System Operating ◽  
Poisson Type

The carotid body impulse generator has been previously characterized as a Poisson-type random process. We examined the validity of this characterization by analyzing sinus nerve spike trains for interspike interval dependency. Fifteen single chemoreceptive afferents were recorded in vivo under hypoxic-hypercapnic conditions, and approximately 1,000 consecutive interspike intervals for each fiber were timed and analyzed for serial dependence. The same set of intervals placed in shuffled order served as a control series without serial dependence. The original spike interval trains showed significantly negative first-order serial correlation coefficients and less variability in joint interval distributions than did the shuffled interval trains. These results suggest that the chemoreceptor afferent train is not random and may reflect a negative feedback system operating within the carotid body that limits variation about a mean frequency.

The surfaces whose prime-sections contain a

1934 ◽  
Vol 30 (2) ◽  
pp. 170-177 ◽  
Author(s):  
J. Bronowski
Keyword(s):  
Hyperelliptic Curves ◽  
Ruled Surfaces ◽  
Minimum Order ◽  
Rational Surfaces ◽  
Pencil Of Conics

The surfaces whose prime-sections are hyperelliptic curves of genus p have been classified by G. Castelnuovo. If p > 1, they are the surfaces which contain a (rational) pencil of conics, which traces the on the prime-sections. Thus, if we exclude ruled surfaces, they are rational surfaces. The supernormal surfaces are of order 4p + 4 and lie in space [3p + 5]. The minimum directrix curve to the pencil of conics—that is, the curve of minimum order which meets each conic in one point—may be of any order k, where 0 ≤ k ≤ p + 1. The prime-sections of these surfaces are conveniently represented on the normal rational ruled surfaces, either by quadric sections, or by quadric sections residual to a generator, according as k is even or odd.

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