The modified Mellin transform Zk(s) = ∫ ∞ 1 |ζ( 1 2 + ix)|x dx (k ∈ N) is used to obtain estimates for

Integral transforms play an important rôle in Analytic number theory, the part of Number theory where problems of a number-theoretic nature are solved by the use of various methods from Analysis. The most common integral transforms that are used are: Mellin transforms (Robert Hjalmar Mellin, 18541933), Laplace transforms (Pierre-Simon, marquis de Laplace, 1749-1827) and Fourier transforms (Jose...

We describe a method for attaching persistent metadata to an image. The method can be interpreted as a template-based blind watermarking scheme, robust to common editing operations, namely: cropping, rotation, scaling, stretching, shearing, compression, printing, scanning, noise, and color removal. Robustness is achieved through the reciprocity of the embedding and detection invariants. The emb...

In this paper, we define a (p, v)-extension of Hurwitz-Lerch Zeta function by considering an extension of beta function defined by Parmar et al. [J. Classical Anal. 11 (2017) 81106]. We obtain its basic properties which include integral representations, Mellin transformation, derivative formulas and certain generating relations. Also, we establish the special cases of the main results. keywords...

this article is devoted to study of the autoconvolution equations and generalized mittag-leffler functions. these types of equations are given in terms of the laplace transform convolution of a function with itself. we state new classes of the autoconvolution equations of the first kind and show that the generalized mittag-leffler functions are solutions of these types of equations. in view of ...

The fundamental solution (Green function) for the Cauchy problem of the space-time fractional diffusion equation is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. Then, by using the Mellin transform, a general representation of the Green function in terms of Mellin-Barnes integrals in the complex plane is derived. This allow...

The optical Mellin transform has recently been success­ fully realized and used to construct useful scale invariant optical pattern recognition systems, in Doppler signal pro­ cessing, and in the correlation of nonvertical imagery, among other applications. The Mellin transform of f(x) can be synthesized optically by applying a coordinate transformation ξ = lnx to the input coordinate x and an ...

We can recognize vowel sounds regardless of whether a man, woman or child pronounces them. Such vowel normalization has proved to be a difficult task for computer models to simulate. Motivated by observations of the auditory system Irino and Patterson have discussed the stabilized wavelet Mellin transform as a candidate method for vowel normalization. The aim of this paper is to quantify and ex...