Prime chains and Pratt trees (2009)
Ford, Kevin, Konyagin, Sergei V., Luca, Florian
We study the distribution of prime chains, which are sequences p_1,...,p_k of primes for which p_{j+1}\equiv 1\pmod{p_j} for each j. We first give conditional upper bounds on the length of Cunningham...
The Erdos-Turan problem in infinite groups (2009)
Konyagin, Sergei V., Lev, Vsevolod F.
Let $G$ be an infinite abelian group with $|2G|=|G|$. We show that if $G$ is not the direct sum of a group of exponent 3 and the group of order 2, then $G$ possesses a perfect additive basis; that...
Convergence of greedy approximation for the trigonometric system, Analys (2008)
Abstract. In this note we discuss the convergence of greedy approximants for trigonometric Fourier expansion in Lp(T), 1 ≤ p < 2. 1.
ON THE DISTRIBUTION OF EXPONENTIAL SUMS (2008)
Sergei V. Konyagin, Vsevolod F. Lev
We discuss three problems of the following kind: given a set A ⊆ Fp of n: = |A | residues modulo a prime p, how are the absolute values |SA(z) | of the corresponding exponential sums distributed in...
Bourgain, Jean, Konyagin, Sergei V., Shparlinski, Igor E.
We give a lower bound on the size of the product set of two arbitrary subsets of the set of Farey fractions of a given order and apply it to study the distribution of elements of multiplicative...
On the Distribution of Pseudopowers (2007)
Konyagin, Sergei V., Pomerance, Carl, Shparlinski, Igor E.
An $x$-pseudopower to base $g$ is a positive integer which is not a power of $g$ yet is so modulo $p$ for all primes $p\le x$. We improve an upper bound for the least such number due to E. Bach, R....
Sums of products of congruence classes and of arithmetic progressions (2007)
Konyagin, Sergei V., Nathanson, Melvyn B.
Consider the congruence class R_m(a)={a+im:i\in Z} and the infinite arithmetic progression P_m(a)={a+im:i\in N_0}. For positive integers a,b,c,d,m the sum of products set R_m(a)R_m(b)+R_m(c)R_m(d)...
Incomplete exponential sums and Diffie-Hellman triples (2006)
Banks, William D, Friedlander, John B, Konyagin, Sergei V, Shparlinski, Igor E
Let p be a prime and ϑ an integer of order t in the multiplicative group modulo p. In this paper, we continue the study of the distribution of Diffie–Hellman triples (ϑx, ϑy, ϑxy ) by...