  We find an explicit upper bound for general $L$-functions on the critical
line, assuming the Generalized Riemann Hypothesis, and give as illustrative
examples its application to some families of $L$-functions and Dedekind zeta
functions. Further, this upper bound is used to obtain lower bounds beyond
which all eligible integers are represented by Ramanujan's ternary form and
Kaplansky's ternary forms. This improves on previous work of Ono and
Soundararajan on Ramanujan's form and Reinke on Kaplansky's form with a
substantially easier proof.
