skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: The error term in the truncated Perron formula for the logarithm of an L -function
Abstract We improve upon the traditional error term in the truncated Perron formula for the logarithm of anL-function. All our constants are explicit.  more » « less
Award ID(s):
2054002
PAR ID:
10503833
Author(s) / Creator(s):
; ;
Publisher / Repository:
Canadian Mathematical Bulletin
Date Published:
Journal Name:
Canadian Mathematical Bulletin
Volume:
66
Issue:
4
ISSN:
0008-4395
Page Range / eLocation ID:
1122 to 1134
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract We construct the Neumann function in a 1-sided chord-arc domain (i.e., a uniform domain with an Ahlfors regular boundary), and establish size and Hölder continuity estimates up to the boundary. We then obtain a Kenig-Pipher type theorem, in whichLpsolvability of the Neumann problem is shown to yield solvability inLqfor 1 <q<p, and in the Hardy spaceH1, in 2-sided chord-arc domains, under suitable background hypotheses. 
    more » « less
  2. Summary The timing of insects’ daily (feeding, movement) and seasonal (diapause, migration) rhythms affects their population dynamics and distribution. Yet, despite their implications for insect conservation and pest management, the genetic mechanisms underlying variation in timing are poorly understood. Prior research in the European corn borer moth (Ostrinia nubilalis) associated ecotype differences in seasonal diapause and daily activity with genetic variation at the circadian clock geneperiod(per). Here, we demonstrate that populations with divergent allele frequencies atperexhibit differences in daily behavior, seasonal development, and the expression of circadian clock genes. Specifically, later daily activity and shortened diapause were associated with a reduction and delay in the abundance of cyclingpermRNA. CRISPR/Cas9-mediated mutagenesis revealed thatperand/or an intact circadian clock network were essential for the appropriate timing of daily behavior and seasonal responsiveness. Furthermore, a reduction ofpergene dosage inperheterozygous mutants (per-/+) pleiotropically decreased the diapause incidence, shortened post-diapause development, and delayed the timing of daily behavior, in a manner phenotypically reminiscent of wild-type individuals. Altogether, this combination of observational and experimental research strongly suggests thatperis a master regulator of biological rhythms and may contribute to the observed life cycle differences between bivoltine (two generation) and univoltine (one generation)O. nubilalis. HighlightsNatural ecotypes with divergentperiod(per) genotypes differ in their daily and seasonal responses to photoperiodLater daily activity, reduced diapause incidence, and shorter post-diapause development is associated with reducedpermRNA abundanceperis essential for short-day recognition and daily timingReducedpergene dosage shortened post-diapause development and delayed locomotor activity 
    more » « less
  3. Abstract TaxonomyPotato virus Xis the type‐member of the plant‐infectingPotexvirusgenus in the familyAlphaflexiviridae. Physical propertiesPotato virus X (PVX) virions are flexuous filaments 460–480 nm in length. Virions are 13 nm in diameter and have a helical pitch of 3.4 nm. The genome is approximately 6.4 kb with a 5′ cap and 3′ poly(A) terminus. PVX contains five open reading frames, four of which are essential for cell‐to‐cell and systemic movement. One protein encodes the viral replicase. Cellular inclusions, known as X‐bodies, occur near the nucleus of virus‐infected cells. HostsThe primary host is potato, but it infects a wide range of dicots. Diagnostic hosts includeDatura stramoniumandNicotiana tabacum. PVX is transmitted in nature by mechanical contact. Useful websitehttps://talk.ictvonline.org/ictv‐reports/ictv_online_report/positive‐sense‐rna‐viruses/w/alphaflexiviridae/1330/genus‐potexvirus 
    more » « less
  4. PremiseApetaly is widespread across distantly related lineages of flowering plants and is associated with abiotic (or self‐) pollination. It is particularly prevalent in the carnation family, and the cosmopolitan genusStellariacontains many lineages that are hypothesized to have lost petals from showy petalous ancestors. But the pollination biology of apetalous species ofStellariaremains unclear. MethodsUsing a substantial species‐level sampling (~92% of known taxonomic diversity), we describe the pattern of petal evolution withinStellariausing ancestral character state reconstructions. To help shed light on the reproductive biology of apetalousStellaria, we conducted a field experiment at an alpine tundra site in the southern Rocky Mountains to test whether an apetalous species (S. irrigua) exhibits higher levels of selfing than a sympatric, showy petalous congener (S. longipes). ResultsAnalyses indicated that the ancestor ofStellariawas likely showy petalous and that repeated, parallel reductions of petals occurred in clades across much of the world, with uncommon reversal back to showy petals. Field experiments supported high rates of selfing in the apetalous species and high rates of outcrossing in the petalous species. ConclusionsPetal loss is rampant across major clades ofStellariaand is potentially linked with self‐pollination worldwide. Self‐pollination occurs within the buds inS. irrigua, and high propensities for this and other forms of selfing known in many other taxa of arctic‐alpine habitats may reflect erratic availability of pollinators. 
    more » « less
  5. Summary Distyly is an intriguing floral adaptation that increases pollen transfer precision and restricts inbreeding. It has been a model system in evolutionary biology since Darwin. Although theS‐locus determines the long‐ and short‐styled morphs, the genes were unknown inTurnera. We have now identified these genes.We used deletion mapping to identify, and then sequence,BACclones and genome scaffolds to constructS/shaplotypes. We investigated candidate gene expression, hemizygosity, and used mutants, to explore gene function.Thes‐haplotype possessed 21 genes collinear with a region of chromosome 7 of grape. TheS‐haplotype possessed three additional genes and two inversions.TsSPH1was expressed in filaments and anthers,TsYUC6in anthers andTsBAHDin pistils. Long‐homostyle mutants did not possessTsBAHDand a short‐homostyle mutant did not expressTsSPH1.Three hemizygous genes appear to determine S‐morph characteristics inT. subulata. Hemizygosity is common to all distylous species investigated, yet the genes differ. The pistil candidate gene,TsBAHD, differs from that ofPrimula, but both may inactivate brassinosteroids causing short styles.TsYUC6is involved in auxin synthesis and likely determines pollen characteristics.TsSPH1is likely involved in filament elongation. We propose an incompatibility mechanism involvingTsYUC6andTsBAHD. 
    more » « less