Geodesic
Distribution of~prime numbers and the discrete spectrum of~the Laplace operator
Izvestiya. Mathematics , Tome 84 (2020) no. 5, pp. 960-977

Voir la notice de l'article provenant de la source Math-Net.Ru

We obtain a class of explicit formulae each of which gives an expression for the remainder term in the asymptotic equation for the Chebyshev function in terms of the spectrum of the Laplace operator on the fundamental domain of the modular group.
Keywords: prime numbers, Chebyshev psi-function, spectrum of the Laplace operator, modular group. 
@article{IM2_2020_84_5_a5,
     author = {D. A. Popov},
     title = {Distribution of~prime numbers and the discrete spectrum of~the {Laplace} operator},
     journal = {Izvestiya. Mathematics },
     pages = {960--977},
     publisher = {mathdoc},
     volume = {84},
     number = {5},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2020_84_5_a5/}
}
TY  - JOUR
AU  - D. A. Popov
TI  - Distribution of~prime numbers and the discrete spectrum of~the Laplace operator
JO  - Izvestiya. Mathematics 
PY  - 2020
SP  - 960
EP  - 977
VL  - 84
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2020_84_5_a5/
LA  - en
ID  - IM2_2020_84_5_a5
ER  - 
%0 Journal Article
%A D. A. Popov
%T Distribution of~prime numbers and the discrete spectrum of~the Laplace operator
%J Izvestiya. Mathematics 
%D 2020
%P 960-977
%V 84
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2020_84_5_a5/
%G en
%F IM2_2020_84_5_a5
D. A. Popov. Distribution of~prime numbers and the discrete spectrum of~the Laplace operator. Izvestiya. Mathematics , Tome 84 (2020) no. 5, pp. 960-977. http://geodesic.mathdoc.fr/item/IM2_2020_84_5_a5/