Geodesic
On one generalization of the Plan formula
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2018), pp. 41-51 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We obtain an analog of the Plan formula, which is essential in obtaining a functional relation to the classical Riemann zeta-function.
Mots-clés : Plan formula
Keywords: entire function, integral representation. 
@article{IVM_2018_5_a5,
     author = {V. I. Kuzovatov},
     title = {On one generalization of the {Plan} formula},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {41--51},
     year = {2018},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_5_a5/}
}
TY  - JOUR
AU  - V. I. Kuzovatov
TI  - On one generalization of the Plan formula
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2018
SP  - 41
EP  - 51
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/IVM_2018_5_a5/
LA  - ru
ID  - IVM_2018_5_a5
ER  - 
%0 Journal Article
%A V. I. Kuzovatov
%T On one generalization of the Plan formula
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2018
%P 41-51
%N 5
%U http://geodesic.mathdoc.fr/item/IVM_2018_5_a5/
%G ru
%F IVM_2018_5_a5
V. I. Kuzovatov. On one generalization of the Plan formula. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2018), pp. 41-51. http://geodesic.mathdoc.fr/item/IVM_2018_5_a5/

[1] Whittaker E. T., Watson G. N., A course of modern analysis, Cambridge University Press, Cambridge, 1927 | MR

[2] Titchmarsh E. C., The theory of the Riemann zeta-function, Oxford University Press, Oxford, 1951 | MR

[3] Kuzovatov V. I., Kytmanov A. M., “Ob odnom analoge formuly Plana”, Izv. NAN Armenii. Matem., 53:3 (2018), 1–12

[4] Gelfand I. M., Levitan B. M., “Ob odnom prostom tozhdestve dlya sobstvennykh znachenii differentsialnogo operatora vtorogo poryadka”, DAN SSSR, 88:4 (1953), 593—596

[5] Dikii L. A., “Dzeta-funktsiya obyknovennogo differentsialnogo uravneniya na konechnom otrezke”, Izv. AN SSSR. Ser. matem., 19:4 (1955), 187—200

[6] Dikii L. A., “Formuly sledov dlya differentsialnykh operatorov Shturma–Liuvillya”, UMN, 13:3 (1958), 111—143

[7] Lidskii V. B., Sadovnichii V. A., “Regulyarizovannye summy kornei odnogo klassa tselykh funktsii”, Funkts. analiz i ego prilozh., 1:2 (1967), 52–59

[8] Smagin S. A., Shubin M. A., “O dzeta-funktsii transversalno ellipticheskogo operatora”, UMN, 39:2 (1984), 187–188

[9] Kytmanov A. M., Myslivets S. G., “O dzeta-funktsii sistem nelineinykh uravnenii”, Sib. matem. zhurn., 48:5 (2007), 1073–1082 | MR

[10] Kuzovatov V. I., Kytmanov A. A., “On the zeta-function of zeros of some class of entire functions”, J. Siberian Federal Univ. Math. Phys., 7:4 (2014), 489—499 | DOI

[11] Bieberbach L., Analytische Fortsetzung, Springer-Verlag, Berlin, 1955 | MR