Explicit Upper Bounds for L-functions on the critical line

Details Explicit Upper Bounds for L-functions on the critical line Explicit Upper Bounds for L-functions on the critical line

2009-06-23

arxiv.org/abs/0906.4177v1

Mathematics

Number Theory

Scientific paper

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.

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