Large values of certain number-theoretic error terms

Estimates of convolutions of certain number-theoretic error terms

Several estimates for the convolution function C[f (x)] := x 1 f (y)f (x/y)(dy/y) and its iterates are obtained when f (x) is a suitable number-theoretic error term. We deal with the case of the asymptotic formula for T 0 |ζ(1/2 + it)| 2k dt (k = 1, 2), the general Dirichlet divisor problem, the problem of nonisomorphic Abelian groups of given order, and the Rankin-Selberg convolution. 1. Convo...

Convolutions and Mean Square Estimates of Certain Number-theoretic Error Terms

We study the convolution function

A Number-Theoretic Error-Correcting Code

In this paper we describe a new error-correcting code (ECC) inspired by the Naccache-Stern cryptosystem. While by far less efficient than Turbo codes, the proposed ECC happens to be more efficient than some established ECCs for certain sets of parameters. The new ECC adds an appendix to the message. The appendix is the modular product of small primes representing the message bits. The receiver ...

On the Complexity of Certain Algebraic and Number Theoretic Problems

Ideal Error-Correcting Codes: Unifying Algebraic and Number-Theoretic Algorithms

Over the past five years a number of algorithms decoding some well-studied error-correcting codes far beyond their “error-correcting radii” have been developed. These algorithms, usually termed as listdecoding algorithms, originated with a list-decoder for Reed-Solomon codes [36, 17], and were soon extended to decoders for Algebraic Geometry codes [33, 17] and as also some number-theoretic code...