On two conjecture of Sierpinski concerning the arithmetic functions
σ and φ , with S. Konyagin.
Number Theory in Progress (Zakopane, Poland 1997), de Gruyter (1999),
795-803.
PS file (170K) ,
DVI file (32K) ,
PDF file (167K) .
Residue classes free of values of Euler's function ,
with S. Konyagin and C. Pomerance. Number Theory in Progress (Zakopane,
Poland 1997), de Gruyter (1999), 805-812.
PS file ,
PDF file ,
The normal behavior of the Smarandache function ,
Smarandache Notions J. 10, no. 1-2-3. (1999), 81--86.
DVI format, PDF format. Note: This paper was neither submitted to, nor refereed by, this journal.
ERRATA: The constants appearing in Theorem 1 and Corollary 3 are incorrect.
The factors 1+log 2 should be replaced by 2. The main error is on page 4, equation
(2). The second argument to the second ψ term should be p ,
not q (Thanks to A. Ivic for discovering this).
On an irreducibility theorem of A. Schinzel associated with
coverings of the integers , with M. Filaseta and S. Konyagin.
Illinois J. of Math. 44 (2000), 633-643.
PDF file
Zeros of Dirichlet L-functions near the real axis and
Chebyshev's bias , with C. Bays, R. Hudson and M. Rubinstein.
J. Number Theory 87 (2001), 54-76.
PDF File
The prime number race and zeros of Dirichlet L-functions
off the critical line , with S. Konyagin,
Duke Math. J. 113 (2002), 313-330.
PDF File ,
DVI File .
Zero-free regions for the Riemann zeta function ,
Number Theory for the Millenium (Urbana, IL, 2000), vol. II (2002), 25-56.
PDF File
Maximal collections of intersecting arithmetic progressions
,
Combinatorica 23 (2) (2003), 263-281.
PDF File
The jumping champions of the Farey series ,
with C. Cobeli and A. Zaharescu;
Acta Arithmetica
110 (2003), no. 4, 259--274
PDF file
The prime number race and zeros of Dirichlet L-functions
off the critical line, II , with S. Konyagin, Proceedings of
the session in analytic number theory and Diophantine equations (Bonn,
January--June 2002), Bonner Mathematische Schiften, Nr. 360
(D. R. Heath-Brown, B. Z. Moroz, editors), Bonn, Germany, 2003,
40 pages.
PDF file
From Kolmogorov's theorem on empirical distribution to
number theory , appeared in the book
"Kolmogorov's legacy in mathematics", eds. E. Charpentier et al.,
Editions Belin (Paris),
2004, 111-120. The printed version is in French.
PDF file of English original (8 pages).
See below for an updated version (appeared in the English version of
the book).
From Kolmogorov's theorem on empirical distribution to number
theory . Appeared in the book Kolmogorov's heritage
in mathematics (English edition) , Editions Belin/Springer, 2007,
97-108.
Updated version (with sketch of a different proof of the main result).
PDF file (13 pages).
On the parity of the number
of small divisors of n ,
with F. Luca, C. Pomerance and J. Shallit,
for the book
Analytic Number Theory , in honor of Helmut Maier's 60th
birthday, C. Pomerance and M.Th. Rassias (eds.), Springer-Verlag.