Difference independence of the Riemann zeta function

نویسندگان

  • Yik - Man Chiang
  • Shao - Ji Feng
چکیده

It is proved that the Riemann zeta function does not satisfy any nontrivial algebraic difference equation whose coefficients are meromor-phic functions φ with Nevanlinna characteristic satisfying T (r, φ) = o(r) as r → ∞.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A more accurate half-discrete Hardy-Hilbert-type inequality with the best possible constant factor related to the extended Riemann-Zeta function

By the method of weight coefficients, techniques of real analysis and Hermite-Hadamard's inequality, a half-discrete Hardy-Hilbert-type inequality related to the kernel of the hyperbolic cosecant function with the best possible constant factor expressed in terms of the extended Riemann-zeta function is proved. The more accurate equivalent forms, the operator expressions with the norm, the rever...

متن کامل

Frobenius Difference Equations and Algebraic Independence of Zeta Values in Positive Equal Characteristic

In analogy with the Riemann zeta function at positive integers, for each finite field Fpr with fixed characteristic p we consider Carlitz zeta values ζr(n) at positive integers n. Our theorem asserts that among the zeta values in ∪∞ r=1 {ζr(1), ζr(2), ζr(3), . . . }, all the algebraic relations are those relations within each individual family {ζr(1), ζr(2), ζr(3), . . . }. These are the algebr...

متن کامل

Irrationality of values of the Riemann zeta function

The paper deals with a generalization of Rivoal’s construction, which enables one to construct linear approximating forms in 1 and the values of the zeta function ζ(s) only at odd points. We prove theorems on the irrationality of the number ζ(s) for some odd integers s in a given segment of the set of positive integers. Using certain refined arithmetical estimates, we strengthen Rivoal’s origin...

متن کامل

Algebraic Independence of Carlitz Zeta Values with Varying Constant Fields

As an analogue to special values at positive integers of the Riemann zeta function, for each constant field Fpr with fixed characteristic p we consider Carlitz zeta values ζr(n) at positive integers n. The main theorem of this paper asserts that among the families of Carlitz zeta values ∪∞ r=1 {ζr(1), ζr(2), ζr(3), . . . }, all the algebraic relations are those algebraic relations among each in...

متن کامل

Spectral spacing correlations for chaotic and disordered systems

New aspects of spectral fluctuations of (quantum) chaotic and diffusive systems are considered, namely autocorrelations of the spacing between consecutive levels or spacing autocovariances. They can be viewed as a discretized two point correlation function. Their behavior results from two different contributions. One corresponds to (universal) random matrix eigenvalue fluctuations, the other to...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2006