Publications in Scientific Journals:
M. Drmota, C. Mauduit, J. Rivat:
"Prime numbers in two bases";
Duke Mathematical Journal,
169
(2020),
10;
1809
- 1876.
English abstract:
We estimate the sums ?n=x?(n)f(n)g(n)exp(2ip?n)
and ?n=xµ(n)f(n)g(n)exp(2ip?n),
where ? denotes the von Mangoldt function (and µ the Möbius function) whenever q1 and q2 are two coprime bases, f (resp., g) is a strongly q1-multiplicative (resp., strongly q2-multiplicative) function of modulus 1, and ? is a real number. The goal of this work is to introduce a new approach to study these sums involving simultaneously two different bases combining Fourier analysis, Diophantine approximation, and combinatorial arguments. We deduce from these estimates a prime number theorem (and Möbius orthogonality) for sequences of integers with digit properties in two coprime bases.
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1215/00127094-2019-0083
Created from the Publication Database of the Vienna University of Technology.