On two conjectures of Sierpiński concerning the (2008)
arithmetic functions σ and φ
On A Limit Point Associated With The abc-Conjecture (2007)
Michael Filaseta, Sergei Konyagin, Theorem S
9.89> T 1; 3 2 ' 6= ;. In other words, we prove that there is a limit point of fL a;b g somewhere in the interval [1; 3=2). Before proving the theorem, it is of some value to discuss simpler...
Sergei Konyagin, Communicated Wan Daging
We prove an asymptotic formula for the number of permutations for which the associated permutation polynomial has degree smaller than q Science (USA) 2. # 2002 Elsevier Let Fq be a finite field with...
On the Littlewood problem modulo a prime (2006)
Let p be a prime, and let f : Z/pZ -> R be a function with average value 0 and ||f||_A > (log p)^{1/3 - eps}. This gives a result on a ``mod p'' analogue of Littlewood's well-known problem concerning...
SIEVING BY LARGE INTEGERS AND COVERING SYSTEMS OF CONGRUENCES (2006)
Michael Filaseta, Sergei Konyagin, Gang Yu, Kevin Ford, Carl Pomerance
An old question of Erdős asks if there exists, for each number N, a finite set S of integers greater than N and residue classes r(n) (mod n) for n ∈ S whose union is Z. We prove that if � n∈S...
Sieving by large integers and covering systems of congruences (2005)
Filaseta, Michael, Ford, Kevin, Konyagin, Sergei, Pomerance, Carl, Yu, Gang
An old question of Erdos asks if there exists, for each number N, a finite set S of integers greater than N and residue classes r(n) mod n for n in S whose union is all the integers. We prove that if...
Separated sets and the Falconer conjecture for polygonal norms (2004)
Konyagin, Sergei, Laba, Izabella
The Falconer conjecture asserts that if E is a planar set with Hausdorff dimension strictly greater than 1, then its Euclidean distance set has positive one-dimensional Lebesgue measure. We discuss...
Distance sets of well-distributed planar sets for polygonal norms (2004)
Konyagin, Sergei, Laba, Izabella
Let X be a 2-dimensional normed space, and let BX be the unit ball in X. We discuss the question of how large the set of extremal points of BX must be if X contains a well-distributed set whose...
Spectra of Certain Types of Polynomials and Tiling of Integers with Translates of Finite Sets (2004)
The Erwin, Schrödinger International Boltzmanngasse, Sergei Konyagin, Sergei Konyagin
Available via anonymous ftp from FTP.ESI.AC.AT or via WWW,
Enumerating Permutation Polynomials Over Finite Fields By Degree Ii (2003)
Sergei Konyagin, Francesco Pappalardi
This note is an appendix to a paper by the same authors that appeared in 2002 in the same journal. First we extend the method of the result of the previous paper proving an asymptotic formula for the...
Spectra of certain types of polynomials and tiling of integers with translates of finite sets (2002)
Konyagin, Sergei, Laba, Izabella
We consider two number-theoretic problems arising from Fuglede's spectral set conjecture: characterizing finite sets that tile integers, and finding polynomials with (0,1) coefficients whose roots...
The prime number race and zeros of L-functions off the critical line (2002)
We examine the effects of certain hypothetical configurations of zeros of Dirichlet L-functions lying off the critical line on the distribution of primes in arithmetic progressions.
Sergei Konyagin, Izabella Laba, Sergei Konyagin, Izabella Laba
Spectra of certain types of polynomials and tiling of integers with translates of finite sets
Enumerating Permutation Polynomials over finite fields by degree (2001)
Konyagin, Sergei, Pappalardi, Francesco
We prove an asymptotic formula for the number of permutation for which the associated permutation polynomial has degree smaller than $q-2$.
Residue classes free of values of Euler’s function (1999)
Kevin Ford, Sergei Konyagin, Carl Pomerance
Dedicated to Andrzej Schinzel on his sixtieth birthday By a totient we mean a value taken by Euler’s function φ(n). Dence and Pomerance [DP] have established Theorem A. If a residue class contains...
Squarefree Values Of Polynomials All Of Whose Coefficients Are 0 And 1 (1996)
Michael Filaseta, Sergei Konyagin
this paper is to establish two results concerning the polynomials in S.