A Lemma in complex function theory I
Balasubramanian, R ; Ramachandra, K
HAL, hal-01104337 / Harvested from HAL
Text on HAL
Continuing our earlier work on the same topic published in the same journal last year we prove the following result in this paper: If $f(z)$ is analytic in the closed disc $\vert z\vert\leq r$ where $\vert f(z)\vert\leq M$ holds, and $A\geq1$, then $\vert f(0)\vert\leq(24A\log M) (\frac{1}{2r}\int_{-r}^r \vert f(iy)\vert\,dy)+M^{-A}.$ Proof uses an averaging technique involving the use of the exponential function and has many applications to Dirichlet series and the Riemann zeta function.
Publié le : 1989-07-04
Classification:  analytic function,  semi-circular portion,  [MATH]Mathematics [math] 
@article{hal-01104337,
     author = {Balasubramanian, R and Ramachandra, K},
     title = {A Lemma in complex function theory I},
     journal = {HAL},
     volume = {1989},
     number = {0},
     year = {1989},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01104337}
}

Balasubramanian, R; Ramachandra, K. A Lemma in complex function theory I. HAL, Tome 1989 (1989) no. 0, . http://gdmltest.u-ga.fr/item/hal-01104337/