A note on entire dirichlet series of irregular growth

Authors : Satendra K VAISH

Pages : 0-0

Doi:10.1501/Commua1_0000000582

View : 36 | Download : 8

Publication Date : 1984-01-01

Article Type : Research Paper

Abstract :F or an entire Dirichlet series finsert ignore into journalissuearticles values(s); — S an expinsert ignore into journalissuearticles values(s Xn );, insert ignore into journalissuearticles values(s = a -H it, 0 < X: < X2 Xa < . . . 5 Üm sup ? = O);, the order pinsert ignore into journalissuearticles values(O < p < co ); and lower n -*°° Xn Xinsert ignore into journalissuearticles values(O < X < co ); are given by the limit superior and limit inferior of insert ignore into journalissuearticles values(log log Minsert ignore into journalissuearticles values(a););/a, as a -► a» , respectively, where Minsert ignore into journalissuearticles values(o); — sup ] ]finsert ignore into journalissuearticles values(a -f- it);}: -co < t < c©}. In this note w e derive a formula for lower proximate type T \ { — Hm inf insert ignore into journalissuearticles values(log M insert ignore into journalissuearticles values(G ););/e ° ^ [, O < Tx çy-JOO < oo, O < X < c o ,in terms of the coefficients a’n s and X’n s. Here Xinsert ignore into journalissuearticles values(o); is the lower proximate order or finsert ignore into journalissuearticles values(s);.
Keywords : entire, dirichlet, irregular

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