Kotyada Srinivas

On the Uniform Distribution of Certain Sequences

We investigate the uniform distribution of the sequence nα as n ranges over the natural numbers and α is a fixed positive real number which is not an integer. We then apply this in conjunction with the Linnik-Vaughan method to study the uniform distribution of the sequence pα as p ranges over the prime numbers.

Counting squarefree discriminants of trinomials under abc

For an odd positive integer n ≥ 5, assuming the truth of the abc conjecture, we show that for a positive proportion of pairs (a, b) of integers the trinomials of the form t n + at + b (a, b ∈ Z) are irreducible and their discriminants are squarefree.

GAPS BETWEEN THE ZEROS OF EPSTEIN'S ZETA-FUNCTIONS ON THE CRITICAL LINE

It is proved that Epstein’s zeta-function ζQ(s) related to a positive definite integral binary quadratic form has a zero 1 2 + iγ with T ≤ γ ≤ T + T 5/11+e for sufficiently large positive numbers T . This improves a classical result of H. S. A. Potter and E. C. Titchmarsh. To Professor K. Ramachandra on his seventieth birthday

A ZERO DENSITY ESTIMATE FOR THE SELBERG CLASS

It is well known that bounds on moments of a specific L-function can lead to zero-density result for that L-function. In this paper, we generalize this argument to all L-functions in the Selberg class by assuming a certain second power moment. As an application, it is shown that in the case of symmetric-square L-function, this result improves the existing one.

Digital watermarking: An approach based on Hilbert transform

Most of the well known algorithms for watermarking of digital images involve transformation of the image data to Fourier or singular vector space. In this paper, we introduce watermarking in Hilbert transform domain for digital media. Hilbert transform provides an analytic representation of a signal in terms of a phase and amplitude function. In this work, we apply one-dimensional Hilbert transform on each of the vectors that define an image and embed the watermark in its phase. Based on this idea, we propose an algorithm for embedding and extracting watermark in a host image and analytically obtain a parameter related to this procedure. Using extensive simulations, we show that the algorithm performs well even if the host image is corrupted by various attacks.