Extreme values of quadratic Dirichlet L-functions over function fields
Gopal Maiti
I2M, CNRS & Indian Statistical Institute, Kolkata
https://arxiv.org/search/math?searchtype=author&query=Maiti%2C+G
Date(s) : 28/03/2023 iCal
11h00 - 12h00
We prove an Ω-result for the quadratic Dirichlet L-function |L(1/2, χP)|, where χP is a quadratic Dirichlet character of modulo irreducible polynomials P associated with hyperelliptic curve of genus g over a fixed finite field 𝔽q in the large genus limit. In particular, we showed that for any ε∈(0, 1/2),
maxP∈𝓟2g+1 |L(1/2, χP)| ≪ exp( (1/√2 – ε) (ln q) (g (ln ln g) / ln g)½)
This is recent joint work with Pranendu Darbar.
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