Explicit bounds for products of primes in AP

Autor: Ramachandran Balasubramanian, Olivier Ramaré, Priyamvad Srivastav

Publikováno v: Mathematics of Computation. 92:2381-2411

For all q ≥ 2 q\ge 2 and for all invertible residue classes a a modulo q q , there exists a natural number that is congruent to a a modulo q q and that is the product of exactly three primes, all of which are below ( 10 15 q ) 5 / 2 (10^{15}q)^{5/2

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::db91c7c919c5fd8f8e2b3bb78bd5b0e0
https://doi.org/10.1090/mcom/3853

Product of primes in arithmetic progressions

Autor: Oriol Serra, Olivier Ramaré, Priyamvad Srivastav

Publikováno v: International Journal of Number Theory
International Journal of Number Theory, World Scientific Publishing, 2020, 16 (04), pp.747-766. ⟨10.1142/S1793042120500384⟩
International Journal of Number Theory, 2020, 16 (04), pp.747-766. ⟨10.1142/S1793042120500384⟩
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

We prove that, for all [Formula: see text] and for all invertible residue classes [Formula: see text] modulo [Formula: see text], there exists a natural number [Formula: see text] that is congruent to [Formula: see text] modulo [Formula: see text] an

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7197f8d96a400f29a52352e1d854621d
https://hal.archives-ouvertes.fr/hal-02585970/file/footnote-11.pdf

On correlations of certain multiplicative functions

Autor: Sumit Giri, Priyamvad Srivastav, R. Balasubramanian

In this paper, we study sums of shifted products $\sum\limits_{n \leq x} F(n) G(n-h)$ for any $|h| \leq x/2$ and arithmetic functions $F=f*1$ and $G=g*1$, with $f$ and $g$ small. We obtain asymptotic formula for different orders of magnitude of $f$ a

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7031403f9b492dea1c0b9b64a3ea950c
http://arxiv.org/abs/1511.02221