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LARGE VALUES OF L-FUNCTIONS ON THE 1-LINE
- Source :
- Bulletin of the Australian Mathematical Society. 103:230-243
- Publication Year :
- 2020
- Publisher :
- Cambridge University Press (CUP), 2020.
-
Abstract
- We study lower bounds of a general family of L-functions on the $1$ -line. More precisely, we show that for any $F(s)$ in this family, there exist arbitrarily large t such that $F(1+it)\geq e^{\gamma _F} (\log _2 t + \log _3 t)^m + O(1)$ , where m is the order of the pole of $F(s)$ at $s=1$ . This is a generalisation of the result of Aistleitner, Munsch and Mahatab [‘Extreme values of the Riemann zeta function on the $1$ -line’, Int. Math. Res. Not. IMRN2019(22) (2019), 6924–6932]. As a consequence, we get lower bounds for large values of Dedekind zeta-functions and Rankin-Selberg L-functions of the type $L(s,f\times f)$ on the $1$ -line.
- Subjects :
- Generalization
General Mathematics
010102 general mathematics
Order (ring theory)
Type (model theory)
01 natural sciences
General family
Combinatorics
Riemann hypothesis
symbols.namesake
0103 physical sciences
Line (geometry)
symbols
Dedekind cut
010307 mathematical physics
0101 mathematics
Dedekind zeta function
Mathematics
Subjects
Details
- ISSN :
- 17551633 and 00049727
- Volume :
- 103
- Database :
- OpenAIRE
- Journal :
- Bulletin of the Australian Mathematical Society
- Accession number :
- edsair.doi...........017a2dd78e47ec25774db17ed2e3ea0e
- Full Text :
- https://doi.org/10.1017/s0004972720000647