On the mean values of an entire function represented by Dirichlet series
Bajpai, S. K.
Annales de l'Institut Fourier, Tome 21 (1971), p. 31-34 / Harvested from Numdam
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Pour des fonctions entières définies par des séries de Dirichlet, on démontre un théorème relatif à leurs valeurs moyennes, qui généralise des résultats de Kamthan, Juneya et Awasthi.

For entire functions defined by absolutely convergent Dirichlet series, a theorem on their mean values is established which include the results of Kamthan, Juneja and Awasthi.

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     author = {Bajpai, S. K.},
     title = {On the mean values of an entire function represented by Dirichlet series},
     journal = {Annales de l'Institut Fourier},
     volume = {21},
     year = {1971},
     pages = {31-34},
     doi = {10.5802/aif.371},
     mrnumber = {49 \#576},
     zbl = {0212.42103},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1971__21_2_31_0}
}

Bajpai, S. K. On the mean values of an entire function represented by Dirichlet series. Annales de l'Institut Fourier, Tome 21 (1971) pp. 31-34. doi : 10.5802/aif.371. http://gdmltest.u-ga.fr/item/AIF_1971__21_2_31_0/

[1] A. G. Azpeitia, On the maximum modulus and the maximum term of an entire Dirichlet series, Proc Amer. Math. Soc., 12 (1961), 717-721. | MR 23 #A3829 | Zbl 0126.29003

[2] E. Hille, Analytic function theory volume II ; Blaisdell Pub. Comp., 1962. | MR 34 #1490 | Zbl 0102.29401

[3] P. K. Kamthan, On the mean values of entire functions represented by Dirichlet series ; Acta. Math. Acad. Sci. Hung., 15 (1964), 133-136. | MR 29 #2371 | Zbl 0171.04301

[4] P. K. Kamthan, On the mean values of entire function represented by Dirichlet series, ibidem, 16 (1965), 89-92. | MR 31 #1377 | Zbl 0171.04302

[5] P. K. Kamthan, On entire functions represented by Dirichlet series (IV) ; Ann. Inst. Fourier, Grenoble 16 (1966), 209-223. | Numdam | MR 37 #1606 | Zbl 0145.08103

[6] O. P. Juneja, On the mean values of an entire function and its derivatives represented by Dirichlet series, Ann. Polon. Math., 18 (1966), 307-313. | MR 34 #1524 | Zbl 0173.31702

[7] O. P. Juneja and K. N. Awasthi, On the mean values of an entire function and its derivatives represented by Dirichlet series II, Ann. Polon. Math., 22 (1969), 89-96. | MR 39 #5799 | Zbl 0179.38701

[8] S. Mandelbrojt, Dirichlet series, Rice Inst. Pamph, 31, 4 (1944). | MR 6,267e | Zbl 0063.03767

[9] K. Sugimura, Ubertragung einiger Satze aus der Theorie der ganzen Functionen auf Dirichletsche Reihen, Math. Z., 29 (1928-1929), 264-277. | JFM 54.0365.01