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Izv. RAN. Ser. Mat., 1994, Volume 58, Issue 2, Pages 73–92 (Mi izv803)  

This article is cited in 15 scientific papers (total in 15 papers)

On a conjecture of Polya

A. M. Gaisin

Abstract: For entire functions $F(z)$ of finite lower Ritt order, defined by Dirichlet series with positive exponents, a criterion is found for
$$ \ln\sup\limits_{|t|<\infty}|F(\sigma+it)|=[1+o(1)\ln\min\limits_{|t|\leqslant h}|F(\sigma+it)|\quad(0<h<\infty) $$
to hold as $\sigma\to+\infty$ outside some exceptional set.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1995, 44:2, 281–299

Bibliographic databases:

UDC: 517.53
MSC: 30D15
Received: 18.09.1992

Citation: A. M. Gaisin, “On a conjecture of Polya”, Izv. RAN. Ser. Mat., 58:2 (1994), 73–92; Russian Acad. Sci. Izv. Math., 44:2 (1995), 281–299

Citation in format AMSBIB
\by A.~M.~Gaisin
\paper On~a~conjecture of Polya
\jour Izv. RAN. Ser. Mat.
\yr 1994
\vol 58
\issue 2
\pages 73--92
\jour Russian Acad. Sci. Izv. Math.
\yr 1995
\vol 44
\issue 2
\pages 281--299

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    This publication is cited in the following articles:
    1. A. M. Gaisin, “An estimate of a Dirichlet series with real coefficients on a ray”, Math. Notes, 60:6 (1996), 611–621  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. A. M. Gaisin, I. D. Latypov, “Asymptotics of the logarithm of the maximal term of a modified Dirichlet series”, Russian Math. (Iz. VUZ), 46:9 (2002), 13–22  mathnet  mathscinet  zmath  elib
    3. A. M. Gaisin, “Estimates of the growth and decrease on curves of an entire function of infinite order”, Sb. Math., 194:8 (2003), 1167–1194  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. A. M. Gaisin, I. D. Latypov, “An estimate for the Dirichlet series with Fejér gaps on the real axis”, Siberian Math. J., 45:1 (2004), 53–68  mathnet  crossref  mathscinet  zmath  isi  elib
    5. A. M. Gaisin, I. D. Latypov, “Asymptotic Behavior of the Sum of the Dirichlet Series of Prescribed Growth on Curves”, Math. Notes, 78:1 (2005), 33–46  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. N. N. Yusupova, “Estimation on curves of Dirichlet series with a convex growth majorant”, Russian Math. (Iz. VUZ), 53:5 (2009), 38–47  mathnet  crossref  zmath  elib
    7. A. M. Gaisin, N. N. Yusupova, “Povedenie summy ryada Dirikhle s zadannoi mazhorantoi rosta na krivykh”, Ufimsk. matem. zhurn., 1:2 (2009), 17–28  mathnet  zmath  elib
    8. A. M. Gaisin, Zh. G. Rakhmatullina, “Povedenie minimuma modulya ryada Dirikhle na sisteme otrezkov”, Ufimsk. matem. zhurn., 2:3 (2010), 39–45  mathnet  zmath  elib
    9. A. M. Gaisin, Zh. G. Rakhmatullina, “An estimate for the sum of a Dirichlet series in terms of the minimum of its modulus on a vertical line segment”, Sb. Math., 202:12 (2011), 1741–1773  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. N. N. Aitkuzhina, “Asymptotic growth on curves of a Dirichlet series with regular dominant on a sequence of points”, Siberian Math. J., 53:2 (2012), 193–200  mathnet  crossref  mathscinet  isi
    11. N. N. Aitkuzhina, A. M. Gaisin, “Dirichlet series with real coefficients”, Ufa Math. J., 5:3 (2013), 3–10  mathnet  crossref  elib
    12. A. M. Gaisin, “Minimum of modulus of the sum of Dirichlet series converging in a half-plane”, Ufa Math. J., 5:4 (2013), 49–57  mathnet  crossref  elib
    13. V. B. Sherstyukov, “Distribution of the zeros of canonical products and weighted condensation index”, Sb. Math., 206:9 (2015), 1299–1339  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    14. K. G. Malyutin, “Interpolyatsionnye zadachi tipa A. F. Leonteva”, Kompleksnyi analiz, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 153, VINITI RAN, M., 2018, 108–127  mathnet  mathscinet
    15. V. B. Sherstyukov, “Asimptoticheskie svoistva tselykh funktsii s zadannym zakonom raspredeleniya kornei”, Kompleksnyi analiz. Tselye funktsii i ikh primeneniya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 161, VINITI RAN, M., 2019, 104–129  mathnet  mathscinet
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