Abstract
In the late 1990s, Atle Selberg invented a new method, which had allowed him to prove that if a linear combination of Dirichlet L-functions satisfies a functional equation, then a positive proportion of its zeros lie on the critical line. The paper considers this method in detail for the general case of a linear combination of L-functions from the Selberg class and applies it to a linear combination of L-functions from the Selberg class of degree 2.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Selberg, in Collected Papers (Springer-Verlag, Berlin, 1991), Vol. 2, pp. 47–63.
I. S. Rezvyakova, Dokl. Math. 81, 303–308 (2010).
A. Selberg, Skr. Norske Vid. Akad. 10, 1–59 (1942).
J. L. Hafner, Math. Ann. 264, 21–37 (1983).
I. S. Rezvyakova, Math. Notes 88 (3), 423–439 (2010).
H. Davenport and H. Heilbronn, J. London Math. Soc. 11, 181–185; 307–312 (1936).
S. M. Voronin, Doctoral Dissertation in Mathematics and Physics (Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk, Moscow, 1977).
S. M. Voronin, Izv. Akad. Nauk SSSR, Ser. Mat. 44 (1), 63–91 (1980).
A. A. Karatsuba, Izv. Akad. Nauk SSSR, Ser. Mat. 54 (2), 303–315 (1990).
I. S. Rezvyakova, Izv. Math. 74 (6), 1277–1314 (2010).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © I.S. Rezvyakova, 2015, published in Doklady Akademii Nauk, 2015, Vol. 463, No. 3, pp. 270–273.
Rights and permissions
About this article
Cite this article
Rezvyakova, I.S. Selberg’s method in the problem about the zeros of linear combinations of L-functions on the critical line. Dokl. Math. 92, 448–451 (2015). https://doi.org/10.1134/S1064562415040158
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064562415040158