On the discrepancy estimate of normal numbers
On the Discrepancy of Convex Plane Sets.
On the discrepancy of inversive congruential pseudorandom numbers with prime power modulus.
On the discrepancy of inversive congruential pseudorandom numbers with prime power modulus, II.
On the discrepancy of Markov-normal sequences
We construct a Markov normal sequence with a discrepancy of . The estimation of the discrepancy was previously known to be .
On the discrepancy of (nα)
On the discrepancy of quasi-progressions.
On the discrepancy of sequences associated with the sum-of-digits function
If denotes the sequence of best approximation denominators to a real , and denotes the sum of digits of in the digit representation of to base , then for all irrational, the sequence is uniformly distributed modulo one. Discrepancy estimates for the discrepancy of this sequence are given, which turn out to be best possible if has bounded continued fraction coefficients.
On the discrepancy of some hybrid sequences
On the discrete logarithm problem for plane curves
In this article the discrete logarithm problem in degree 0 class groups of curves over finite fields given by plane models is studied. It is proven that the discrete logarithm problem for non-hyperelliptic curves of genus 3 (given by plane models of degree 4) can be solved in an expected time of , where is the cardinality of the ground field. Moreover, it is proven that for every fixed natural number the following holds: We consider the discrete logarithm problem for curves given by plane models...
On the Dispersion Spectrum.
On the dispersions of the polynomial maps over finite fields.
On the distance between generalized Fibonacci numbers
For an integer k ≥ 2, let be the k-Fibonacci sequence which starts with 0,..., 0,1 (k terms) and each term afterwards is the sum of the k preceding terms. This paper completes a previous work of Marques (2014) which investigated the spacing between terms of distinct k-Fibonacci sequences.
On the distributation of p ... modulo one.
On the distribution function of certain sequences (mod 1)
On the distribution in the arithmetic progressions of reducible quadratic polynomials in short intervals, II
This paper gives further results about the distribution in the arithmetic progressions (modulo a product of two primes) of reducible quadratic polynomials in short intervals , where now . Here we use the Dispersion Method instead of the Large Sieve to get results beyond the classical level , reaching (thus improving also the level of the previous paper, i.e. ), but our new results are different in structure. Then, we make a graphical comparison of the two methods.
On the distribution modulo 1 of the sequence
On the distribution of additive arithmetic functions
On the distribution of algebraic numbers with prescribed factorization properties
On the distribution of amicable numbers.