We study a subtle inequity in the distribution of unnormalized differences between imaginary parts of zeros of the Riemann zeta function, which was observed by a number of authors. We establish a precise measure which explains the phenomenon, that the location of each Riemann zero is encoded in the distribution of large Riemann zeros. We also extend these results to zeros of more general L-func...

We study so-called real zeros of holomorphic Hecke cusp forms, that is zeros on three geodesic segments on which the cusp form (or a multiple of it) takes real values. Ghosh and Sarnak, who were the first to study this problem, showed that existence of many such zeros follows if many short intervals contain numbers whose all prime factors belong to a certain subset of the primes. We prove new r...

and Applied Analysis 3 real and there is a need to locate their position. Moreover, the usual methods M1 – M3 mentioned before for the study of the zeros of Pn x may not apply at all, when Pn x are complex, or they may need serious modifications. Instead, the M4 method can be used directly. Such a functional analytic methodwas introduced in 10 andwas successfully used in a series of papers by t...

Abstract. We show that if the Riemann Hypothesis is true, then in a region containing most of the right-half of the critical strip, the Riemann zeta-function is well approximated by short truncations of its Euler product. Conversely, if the approximation by products is good in this region, the zeta-function has at most finitely many zeros in it. We then construct a parameterized family of non-a...

Linear operators which (1) preserve the reality of zeros of polynomials having only real zeros and (2) map stable polynomials into stable polynomials are investigated using recently established results concerning the zeros of certain Fox–Wright functions and generalized Mittag-Leffler functions. The paper includes several open problems and questions.  2005 Elsevier Inc. All rights reserved.

Based on work of Alain Connes, I have constructed a spectral interpretation for zeros of L-functions. Here we specialise this construction to the Riemann ζ-function. We construct an operator on a nuclear Fréchet space whose spectrum is the set of non-trivial zeros of ζ. We exhibit the explicit formula for the zeros of the Riemann ζ-function as a character formula.

The relation between the zeros of the partition function and spinodal critical points in Ising models with long-range interactions is investigated. We find that the spinodal is associated with the zeros of the partition function in four-dimensional complex temperature/magnetic field space. The zeros approach the real temperature/magnetic field plane as the range of interaction increases.

The Sturm comparison theorems for second order ODEs are classical results from which information on the properties of the zeros of special functions can be obtained. Sturm separation and comparison theorems are also available for difference-differential systems under oscillatory conditions. The separation theorem provides interlacing information for zeros of some special functions and the compa...

This paper studies the Schrödinger operator with Morse potential Vk(u) = 1 4e 2u + keu on a right half-line [u0,∞), and determines the Weyl asymptotics of eigenvalues for constant boundary conditions at the endpoint u0. In consequence it obtains information on the location of zeros of the Whittaker function Wκ,μ(x), for fixed real parameters κ, x with x > 0, viewed as an entire function in the ...

H.264 video standard is used to achieve high quality video and high data compression when compared to other existing video standards. H.264 uses context-based adaptive variable length coding (CAVLC) to code residual data in Baseline profile.The H.264 bitstream consist of zeros and ones.At one of the decoding stages of contextbased adptive variable length decoder (CAVLD), Total Zeros decoder is ...