How Long to Read Zeta Functions for Two-Dimensional Shifts of Finite Type

How Long Does it Take to Read Zeta Functions for Two-Dimensional Shifts of Finite Type?

It takes the average reader 1 hour to read Zeta Functions for Two-Dimensional Shifts of Finite Type by Jung-Chao Ban

Assuming a reading speed of 250 words per minute. Learn more

Description

This work is concerned with zeta functions of two-dimensional shifts of finite type. A two-dimensional zeta function $\zeta^{0}(s)$, which generalizes the Artin-Mazur zeta function, was given by Lind for $\mathbb{Z}^{2}$-action $\phi$. In this paper, the $n$th-order zeta function $\zeta_{n}$ of $\phi$ on $\mathbb{Z}_{n\times \infty}$, $n\geq 1$, is studied first. The trace operator $\mathbf{T}_{n}$, which is the transition matrix for $x$-periodic patterns with period $n$ and height $2$, is rotationally symmetric. The rotational symmetry of $\mathbf{T}_{n}$ induces the reduced trace operator $\tau_{n}$ and $\zeta_{n}=\left(\det\left(I-s^{n}\tau_{n}\right)\right)^{-1}$. The zeta function $\zeta=\prod_{n=1}^{\infty} \left(\det\left(I-s^{n}\tau_{n}\right)\right)^{-1}$ in the $x$-direction is now a reciprocal of an infinite product of polynomials. The zeta function can be presented in the $y$-direction and in the coordinates of any unimodular transformation in $GL_{2}(\mathbb{Z})$. Therefore, there exists a family of zeta functions that are meromorphic extensions of the same analytic function $\zeta^{0}(s)$. The natural boundary of zeta functions is studied. The Taylor series for these zeta functions at the origin are equal with integer coefficients, yielding a family of identities, which are of interest in number theory. The method applies to thermodynamic zeta functions for the Ising model with finite range interactions.

How long is Zeta Functions for Two-Dimensional Shifts of Finite Type?

Zeta Functions for Two-Dimensional Shifts of Finite Type by Jung-Chao Ban is 60 pages long, and a total of 15,000 words.

This makes it 20% the length of the average book. It also has 18% more words than the average book.

How Long Does it Take to Read Zeta Functions for Two-Dimensional Shifts of Finite Type Aloud?

The average oral reading speed is 183 words per minute. This means it takes 1 hour and 21 minutes to read Zeta Functions for Two-Dimensional Shifts of Finite Type aloud.

What Reading Level is Zeta Functions for Two-Dimensional Shifts of Finite Type?

Zeta Functions for Two-Dimensional Shifts of Finite Type is suitable for students ages 8 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

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