Large values of L-functions from the Selberg class

Christoph Aistleitner*, Lukasz Pankowski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In the present paper we prove lower bounds for L-functions from the Selberg class, by this means improving earlier results obtained by the second author together with Jörn Steuding. We formulate two theorems which use slightly different technical assumptions, and give two totally different proofs. The first proof uses the “resonance method”, which was introduced by Soundararajan, while the second proof uses methods from Diophantine approximation which resemble those used by Montgomery. Interestingly, both methods lead to roughly the same lower bounds, which fall short of those known for the Riemann zeta function and seem to be difficult to be improved. Additionally to these results, we also prove upper bounds for L-functions in the Selberg class and present a further application of a theorem of Chen which is used in the Diophantine approximation method mentioned above.
Original languageEnglish
Pages (from-to)345-364
JournalJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - 2017


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