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Abstract We consider negative moments of quadratic Dirichlet $$L$$–functions over function fields. Summing over monic square-free polynomials of degree $2g+1$ in $$\mathbb{F}_{q}[x]$$, we obtain an asymptotic formula for the $$k^{\textrm{th}}$$ shifted negative moment of $$L(1/2+\beta ,\chi _{D})$$, in certain ranges of $$\beta $$ (e.g., when roughly $$\beta \gg \log g/g $$ and $k<1$). We also obtain non-trivial upper bounds for the $$k^{\textrm{th}}$$ shifted negative moment when $$\log (1/\beta ) \ll \log g$$. Previously, almost sharp upper bounds were obtained in [ 3] in the range $$\beta \gg g^{-\frac{1}{2k}+\epsilon }$$.
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MrpC, a CRP/Fnr homolog, functions as a negative autoregulator during the Myxococcus xanthus multicellular developmental program: Negative autoregulation by MrpC
- Award ID(s):
- 1651921
- PAR ID:
- 10064858
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Molecular Microbiology
- Volume:
- 109
- Issue:
- 2
- ISSN:
- 0950-382X
- Page Range / eLocation ID:
- 245 to 261
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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