A note on entire $L$-functions

TL;DR

This paper provides explicit bounds with constants for objects related to entire $L$-functions in the critical strip, assuming the generalized Riemann hypothesis, focusing on Dirichlet $L$-functions for primitive characters.

Contribution

It offers explicit upper and lower bounds with constants for entire $L$-functions in the critical strip under GRH, including Dirichlet $L$-functions for primitive characters.

Findings

Explicit bounds with constants for entire $L$-functions

Results applicable to Dirichlet $L$-functions for primitive characters

Bounds depend on the generalized Riemann hypothesis

Abstract

In this paper, we exhibit upper and lower bounds with explicit constants for some objects related to entire $L$-functions in the critical strip, under the generalized Riemann hypothesis. The examples include the entire Dirichlet $L$-functions $L(s,\chi)$ for primitive characters $\chi$.