59 research outputs found
ELLIPTIC CURVES AND PARAMODULAR FORMS
No full textThere is a lifting from a non-CM elliptic curve to a cuspidal paramodular newform of degree and weight given by the symmetric cube map. We find a description of the level of in terms of the coefficients of the Weierstrass equation of . In order to compute the paramodular level, we need a detailed description of the local representations of \GL(2,\mathbb{Q}_p) attached to , where is the cuspidal automorphic representation of \GL(2,\mathbb{A}_{\mathbb{Q}}) associated with . We use the available description of the local representations of \GL(2,\mathbb{Q}_p) attached to for and determine the local representation of \GL(2,\mathbb{Q}_3) attached to . In fact, we study the representations of \GL(2, K) attached to for any non-archimedean local field of characteristic and residue characteristic
Constraints on cosmic rays in the Milky Way circumgalactic medium from OVIII observations
No full textWe constrain the cosmic ray (CR) population in the circumgalactic medium
(CGM) of Milky Way by comparing the observations of absorption lines of OVIII
ion with predictions from analytical models of CGM : precipitation (PP) and
isothermal (IT) model. For a CGM in hydrostatic equilibrium, the introduction
of CR suppresses thermal pressure, and affects the OVIII ion abundance. We
explore the allowances given to the ratio of CR pressure to thermal pressure
(), with varying boundary conditions,
CGM mass content, photoionization by extragalactic ultraviolet background and
temperature fluctuations. We find that the allowed maximum values of are
: in the PP model and in the IT model. We also
explore the spatial variation of : rising () or declining
() with radius, where A is the normalization of the profiles. In
particular, the models with declining ratio of CR to thermal pressure fare
better than those with rising ratio with suitable temperature fluctuation
(larger for PP and lower for IT). The declining profiles
allow and in the case of IT and PP models,
respectively, thereby accommodating a large value of in
the central region, but not in the outer regions. These limits, combined with
the limits derived from -ray and radio background, can be useful for
building models of Milky Way CGM including CR population. However, the larger
amount of CR can be packed in cold phase which may be one way to circumvent
these constraints.Comment: 11 pages, 5 figures, 1 table Accepted for publication in ApJ on Apr
22, 202
Local data of rational elliptic curves with non-trivial torsion
No full textBy Mazur's Torsion Theorem, there are fourteen possibilities for the
non-trivial torsion subgroup of a rational elliptic curve. For each ,
such that may have additive reduction at a prime , we consider a
parameterized family of elliptic curves with the property that they
parameterize all elliptic curves which contain in their
torsion subgroup. Using these parameterized families, we explicitly classify
the Kodaira-N\'{e}ron type, the conductor exponent, and the local Tamagawa
number at each prime where has additive reduction. As a
consequence, we find all rational elliptic curves with a -torsion or a
-torsion point that have global Tamagawa number .Comment: 36 pages; incorporates referee's suggestions; final version to appear
in Pacific Journal of Mathematic
Representations attached to elliptic curves with a non-trivial odd torsion point
No full textWe give a classification of the cuspidal automorphic representations attached
to rational elliptic curves with a non-trivial torsion point of odd order. Such
elliptic curves are parameterizable, and in this paper, we find the necessary
and sufficient conditions on the parameters to determine when split or
non-split multiplicative reduction occurs. Using this and the known results on
when additive reduction occurs for these parametrized curves, we classify the
automorphic representations in terms of the parameters.Comment: 17 pages; incorporates referee's suggestions; a small correction to
the statement of Theorem 3.3; final version to appear in Bulletin of the
London Mathematical Societ
Gamma-rays from the circumgalactic medium of M31
No full textWe discuss the production of -rays from cosmic rays (CR) in the
circumgalactic medium (CGM) of Andromeda (M31) in light of the recent detection
of -rays from an annular region of kpc away from the M31
disc. We consider the CRs accelerated as a result of the star-formation in the
M31 disk, which are lifted to the CGM by advection due to outflow and CR
diffusion. The advection time scale due to bulk flow of gas triggered by star
formation activity in the M31 disc is comparable ( Gyr) to the diffusion
time scale with diffusion coefficient cm s for the
propagation of CR protons with energy GeV that are responsible for
the highest energy photons observed. We show that a leptonic origin of the
-rays from cosmic ray (CR) electrons has difficulties, as the inverse
Compton time scale (Myr) is much lower than advection time scale
(Gyr) to reach kpc. Invoking CR electrons accelerated by accretion
shocks in the CGM at kpc does not help since it would lead to
diffuse X-ray features that are not observed. We, therefore, study the
production of -rays via hadronic interaction between CR protons and CGM
gas with the help of numerical two-fluid (thermal + CR) hydrodynamical
simulation. We find that a combination of these mechanisms, that are related to
the star formation processes in M31 in the last Gyr, along with
diffusion and hadronic interaction, can explain the observed flux from the CGM
of M31.Comment: 10 pages, 5 figures, Accepted for publication in MNRAS on May 19,
202
Effect of mixed cropping with lupin (Lupinus albus L.) on growth and nitrogen uptake in pasture grasses grown under manure application
No full textThe use of organic fertilizer is essential to ensure sustainable agricultural production. Because organic fertilizer normally acts as a slow-release fertilizer, improving its nutrient-use efficiency is important, particularly in terms of nitrogen (N) nutrition. In the present study, we attempted to increase the N-use efficiency of cattle farmyard manure (CM) in the cultivation of pasture grasses by mixed cropping with white lupin (Lupinus albus), which has been reported to decompose organic N in its rhizosphere. Timothy (Phleum pratense) and orchard grass (Dactylis glomerata) were cultivated with or without either lupin or soybean (Glycine max) in pots under three different N treatments (CM, ammonium sulfate, or no N). In the CM treatment, growth was higher in grasses cultivated with lupin than in those cultivated alone or with soybean. Moreover, decomposition of soluble organic N and protease activity in the rhizosphere soil of grasses with CM treatment were enhanced by mixed cropping with lupin. Analyses of microbial activity and bacterial community structure using Biolog EcoPlates suggested that the enhanced decomposition of soluble organic N was facilitated by lupin roots rather than by rhizosphere microorganisms
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On counting cuspidal automorphic representations for GSp(4)
No full textArticl
Dimension formulas for Siegel modular forms of level
No full textWe prove several dimension formulas for spaces of scalar-valued Siegel
modular forms of degree with respect to certain congruence subgroups of
level . In case of cusp forms, all modular forms considered originate from
cuspidal automorphic representations of whose
local component at admits non-zero fixed vectors under the principal
congruence subgroup of level . Using known dimension formulas combined with
dimensions of spaces of fixed vectors in local representations at , we
obtain formulas for the number of relevant automorphic representations. These
in turn lead to new dimension formulas, in particular for Siegel modular forms
with respect to the Klingen congruence subgroup of level .Comment: 48 pages. Fixed some typographical errors and improved exposition.
Final version which has been published in Mathematik
Supercongruences Arising from Ramanujan-Sato Series
No full textRecently, the authors with Lea Beneish established a recipe for constructing Ramanujan-Sato series for 1/π, and used this to construct 11 explicit examples of Ramanujan-Sato series arising from modular forms for arithmetic triangle groups of non-compact type. Here, we use work of Chisholm, Deines, Long, Nebe and the third author to prove a general p-adic supercongruence theorem through an explicit connection to CM hypergeometric elliptic curves that provides p-adic analogues of these Ramanujan-Sato series. We further use this theorem to construct explicit examples related to each of our explicit Ramanujan-Sato series examples
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