RUS  ENG
Full version
JOURNALS // Matematicheskii Sbornik

Mat. Sb., 2011, Volume 202, Number 12, Pages 23–56 (Mi sm7725)

An estimate for the sum of a Dirichlet series in terms of the minimum of its modulus on a vertical line segment
A. M. Gaisin, Zh. G. Rakhmatullina

References

1. G. Pólya, “On the minimum modulus of integral functions of order less than unity”, J. London Math. Soc., 1 (1926), 78–86  crossref  zmath  scopus
2. G. Pólya, “Untersuchungen über Lücken und Singularitäten von Potenzreihen”, Math. Z., 29:1 (1929), 549–640  crossref  mathscinet  zmath  scopus
3. W. H. J. Fuchs, “Proof of a conjecture of G. Pólya concerning gap series”, Illinois J. Math., 7 (1963), 661–667  mathscinet  zmath
4. W. K. Hayman, “Angular value distribution of power series with gaps”, Proc. London Math. Soc. (3), 24 (1972), 590–624  crossref  mathscinet  zmath  scopus
5. O. B. Skaskiv, “On the Pólya conjecture concerning the maximum and minimum of the modulus of an entire function of finite order given by a lacunary power series”, Anal. Math., 16:2 (1990), 143–157  crossref  mathscinet  zmath  scopus
6. A. M. Gaǐsin, “On a conjecture of Pólya”, Russian Acad. Sci. Izv. Math., 44:2 (1995), 281–299  mathnet  crossref  mathscinet  zmath  scopus
7. A. M. Gaisin, “Estimates of the growth and decrease on curves of an entire function of infinite order on curves”, Sb. Math., 194:8 (2003), 1167–1194  mathnet  crossref  mathscinet  zmath
8. T. Kövari, “A gap-theorem for entire functions of infinite order”, Michigan Math. J., 12:2 (1965), 133–140  crossref  mathscinet  zmath
9. O. B. Skaskiv, “Pripuscheniya Makintaira pro vidsutnist skinchennikh asimptotichnikh znachen u tsiloï funktsiïżlakunami Feiera”, Vestn. Lvivskogo universitetu. Ser. mekh.-matem., 28 (1987), 80–81  mathscinet
10. A. M. Gaǐsin, “On a theorem of Hayman”, Siberian Math. J., 39:3 (1998), 431–445  mathnet  crossref  mathscinet  zmath  scopus
11. A. J. Macintyre, “Asymptotic paths of integral functions with gap power series”, Proc. London Math. Soc. (3), 2 (1952), 286–296  crossref  mathscinet  zmath  scopus
12. N. N. Yusupova, Asimptotika ryadov Dirikhle zadannogo rosta, Diss. … kand. fiz.-mat. nauk, Bashkirskii gos. un-t, Ufa, 2009
13. M. A. Evgrafov, “Ob odnoi teoreme edinstvennosti dlya ryadov Dirikhle”, UMN, 17:3 (1962), 169–175  mathnet  mathscinet  zmath
14. W. K. Hayman, Meromorphic functions, Oxford Math. Monogr., Clarendon Press, Oxford, 1964  mathscinet  mathscinet  zmath  zmath
15. A. F. Leontev, Ryady eksponent, Nauka, M., 1976  mathscinet  zmath
16. I. Ciorǎnescu, L. Zsidó, “A minimum modulus theorem and applications to ultradifferential operators”, Ark. Mat., 17:1–2 (1979), 153–166  crossref  mathscinet  zmath  adsnasa  scopus
17. A. A. Goldberg, I. V. Ostrovskii, Raspredelenie znachenii meromorfnykh funktsii, Nauka, M., 1970  mathscinet  zmath
18. Sh. I. Strelits, Asimptoticheskie svoistva analiticheskikh reshenii differentsialnykh uravnenii, Mintis, Vilnyus, 1972  mathscinet  zmath
19. T. Murai, “The deficiency of entire functions with Fejér gaps”, Ann. Inst. Fourier (Grenoble), 33:3 (1983), 39–58  crossref  mathscinet  zmath
20. A. M. Gaisin, Asimptoticheskie svoistva funktsii, zadannykh ryadami eksponent, Diss. … dokt. fiz.-mat. nauk, In-t matem. s VTs UNTs RAN, Ufa, 1994
21. A. M. Gaisin, “An estimate for a Dirichlet series whose exponents are zeros of an entire function with irregular behavior”, Russian Acad. Sci. Sb. Math., 81:1 (1995), 163–183  mathnet  crossref  mathscinet  zmath  scopus
22. E. Seneta, Regularly varying functions, Lecture Notes in Math., 508, Springer-Verlag, Berlin–Heidelberg–New York, 1976  crossref  mathscinet  mathscinet  zmath  zmath
23. V. S. Boichuk, “Some properties of a refined order”, Siberian Math. J., 20:2 (1979), 162–167  mathnet  crossref  mathscinet  zmath  zmath  scopus
24. M. N. Sheremeta, Asimptoticheskie svoistva tselykh funktsii, zadannykh stepennymi ryadami i ryadami Dirikhle, Diss. … dokt. fiz.-mat. nauk, Lvovskii gos. un-t im. Iv. Franko, Lvov, 1985
25. M. N. Šeremeta, “Analogues of Wiman's theorem for Dirichlet series”, Math. USSR-Sb., 38:1 (1981), 95–107  mathnet  crossref  mathscinet  zmath  zmath  scopus
26. T. I. Seidman, M. S. Gowda, “Norm dependence of the coefficient map on the window size”, Math. Scand., 73:2 (1993), 177–189  mathscinet  zmath
27. K. G. Binmore, “A density theorem with an application to gap power series”, Trans. Amer. Math. Soc., 148:2 (1970), 367–384  crossref  mathscinet  zmath  scopus
28. R. M. Redheffer, “Completeness of sets of complex exponentials”, Advances in Math., 24:1 (1977), 1–62  crossref  mathscinet  zmath  scopus
29. I. F. Krasichkov-Ternovskiǐ, “An interpretation of the Beurling–Malliavin theorem on the radius of completeness”, Math. USSR-Sb., 66:2 (1990), 405–429  mathnet  crossref  mathscinet  zmath  zmath  scopus
30. P. Turán, Eine neue Methode in der Analysis und deren Anwendungen, Akadémiai Kiadó, Budapest, 1953  mathscinet  zmath
31. A. F. Leontev, Posledovatelnosti polinomov iz eksponent, Nauka, M., 1980  mathscinet  zmath
32. N. V. Govorov, “Ob otsenke snizu funktsii, subgarmonicheskoi v kruge”, Teoriya funktsii. funkts. anal. i ikh pril., 1968, no. 6, 130–150  mathscinet  zmath
33. N. S. Landkof, Foundations of modern potential theory, Grundlehren Math. Wiss., 180, Springer-Verlag, Berlin–Heidelberg–New York, 1972  mathscinet  mathscinet  zmath  zmath


© Steklov Math. Inst. of RAS, 2026