Skip to Main content Skip to Navigation
Journal articles

A Lemma in complex function theory I

Abstract : 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.
Document type :
Journal articles
Complete list of metadata

Cited literature [3 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01104337
Contributor : Romain Vanel <>
Submitted on : Friday, January 16, 2015 - 4:41:24 PM
Last modification on : Tuesday, August 11, 2020 - 9:52:15 AM
Long-term archiving on: : Saturday, September 12, 2015 - 6:30:12 AM

File

12Article1.pdf
Explicit agreement for this submission

Identifiers

  • HAL Id : hal-01104337, version 1

Collections

Citation

R Balasubramanian, K Ramachandra. A Lemma in complex function theory I. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 1989, 12, pp.1 - 5. ⟨hal-01104337⟩

Share

Metrics

Record views

260

Files downloads

614