Tuck's incompressibility function: statistics for zeta zeros and eigenvalues
نویسندگان
چکیده
منابع مشابه
Simple Zeros of the Riemann Zeta-function
Assuming the Riemann Hypothesis, Montgomery and Taylor showed that at least 67.25% of the zeros of the Riemann zeta-function are simple. Using Montgomery and Taylor's argument together with an elementary combinatorial argument, we prove that assuming the Riemann Hypothesis at least 67.275% of the zeros are simple.
متن کاملHamiltonian for the Zeros of the Riemann Zeta Function.
A Hamiltonian operator H[over ^] is constructed with the property that if the eigenfunctions obey a suitable boundary condition, then the associated eigenvalues correspond to the nontrivial zeros of the Riemann zeta function. The classical limit of H[over ^] is 2xp, which is consistent with the Berry-Keating conjecture. While H[over ^] is not Hermitian in the conventional sense, iH[over ^] is P...
متن کاملStrong Szegő asymptotics and zeros of the zeta function
Assuming the Riemann hypothesis, we prove the weak convergence of linear statistics of the zeros of L-functions to a Gaussian field, with covariance structure corresponding to the Hnorm of the test functions. For this purpose, we obtain an approximate form of the explicit formula, relying on Selberg’s smoothed expression for ζ′/ζ and the Helffer-Sjöstrand functional calculus. Our main result is...
متن کاملLandau-siegel Zeros and Zeros of the Derivative of the Riemann Zeta Function
We show that if the derivative of the Riemann zeta function has sufficiently many zeros close to the critical line, then the zeta function has many closely spaced zeros. This gives a condition on the zeros of the derivative of the zeta function which implies a lower bound of the class numbers of imaginary quadratic fields.
متن کاملOn the Multiplicity of Zeros of the Zeta-function
A b s t r a c t. Several results are obtained concerning multiplicities of zeros of the Riemann zeta-function ζ(s). They include upper bounds for multiplicities, showing that zeros with large multiplicities have to lie to the left of the line σ = 1. A zero-density counting function involving multiplicities is also discussed. AMS Subject Classification (1991): 11M06
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2008
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/41/38/385202