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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The distribution on periods of the continued fraction of $\sqrt{d}$
$sqrt{d}$ 连续分数 周期
2023/4/18
The continued fraction is a very old and classical object. Its period is closely related to the solubility of the Pell equations, and also to the class group of quadratic fields. Last year, Koymans an...
We show that the coefficients in the Laurent series of the
Igusa local zeta functions I(s) = R
C
f
sω are periods. This is proved by
first showing the existence of functional equation...
Minimum periods of homeomorphisms of orientable surfaces
Minimum periods homeomorphisms orientable surfaces Dynamical Systems
2012/4/17
One of the main problems of the theory of dynamical systems is the determination of the existence of periodic orbits of a self-map and more generally, the structure of the set of periods. Define the m...
Periods of rational maps modulo primes
p-adic dynamics Mordell-Lang conjecture Algebraic Geometry
2011/9/6
Abstract: Let $K$ be a number field, let $\phi \in K(t)$ be a rational map of degree at least 2, and let $\alpha, \beta \in K$. We show that if $\alpha$ is not in the forward orbit of $\beta$, then th...
On Colmez's product formula for periods of CM-abelian varieties
Fermat curve stable reduction product formula
2011/8/25
Abstract: Colmez conjectured a product formula for periods of abelian varieties with complex multiplication by a field K, analogous to the standard product formula in algebraic number theory. He prove...
DEGREES OF PERIODS
DEGREES OF PERIODS
2018/4/19
We introduce the concept of degree to classify the periods in the sense of Kontsevich.Using this notion we give some new understanding of some problems in transcendentalnumber theory.
Periods of Quadratic Twists of Elliptic Curves
Periods Quadratic Twists of Elliptic Curves
2011/1/17
In this paper we prove a relation between the period of an elliptic curve and the period of its real and imaginary quadratic twists. This relation is often misstated in the literature.
Relative trace formulae toward Bessel and Fourier-Jacobi periods of unitary groups
Relative trace formulae Fourier-Jacobi periods of unitary groups
2011/2/24
We propose a relative trace formula approach and state the corresponding fundamental lemma
toward the global restriction problem involving Bessel or Fourier-Jacobi periods of unitary groups Un×Um, ex...
The complex AGM, periods of elliptic curves over C and complex elliptic logarithms
The complex AGM elliptic curves complex elliptic logarithms
2010/11/9
We present a method for computing period lattices and elliptic logarithms for elliptic curves defined over C, using the complex Arithmetic-Geometric Mean (AGM) first studied by Gauss. Earlier authors ...