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$\boldsymbol{L(\sigma ,\chi )}$
In this note, by introducing a new variant of the resonator function, we give an explicit version of the lower bound for
$\log |L(\sigma ,\chi )|$
in the strip
$1/2<\sigma <1$
, which improves the result of Aistleitner et al. [‘On large values of
$L(\sigma ,\chi )$
’, Q. J. Math. 70 (2019), 831–848].
$L$-FUNCTIONS OVER RATIONAL FUNCTION FIELDS
We prove the reciprocity law for the twisted second moments of Dirichlet 
$L$-functions over rational function fields, corresponding to
two irreducible polynomials. This formula is the analogue of the formulas
for Dirichlet 
$L$-functions over 
$\mathbb{Q}$ obtained by Conrey [‘The mean-square of Dirichlet 
$L$-functions’, arXiv:0708.2699 [math.NT] (2007)] and Young [‘The reciprocity law
for the twisted second moment of Dirichlet 
$L$-functions’, Forum Math.
23(6) (2011), 1323–1337].
