140,012 research outputs found
Eichler-Shimura theory for mock modular forms
No full textWe use mock modular forms to compute generating functions for the critical values of modular L-functions, and we answer a generalized form of a question of Kohnen and Zagier by deriving the “extra relation ” that is satisfied by even periods of weakly holomorphic cusp forms. To obtain these results we derive an Eichler-Shimura theory for weakly holomorphic modular forms and mock modular forms. This includes two “Eichler-Shimura isomorphisms”, a “multiplicity two” Hecke theory, a correspondence between mock modular periods and classical periods, and a “Haberland-type” formula which expresses Petersson’s inner product and a related antisymmetric inner product on M!k in terms of periods
Local points on Shimura coverings of shimura curves at bad reduction primes
No full textLet X be the Shimura curve associated with an indefinite rational quaternion algebra of reduced discriminant D > 1. For each prime l dividing D, there is a natural cyclic Galois covering of Shimura curves Y -> X constructed by adding certain level structure at l. The main goal of this note is to study the existence of local points at primes p (not equal to l) of bad reduction on the intermediate curves of these coverings and their Atkin-Lehner quotients
Fine scale eddies in turbulent Taylor-Couette flow up to Re 25 000
No full textReynolds number effects on fine scale eddies in the turbulent Taylor-Couette flow have been investigated by high accuracy direct numerical simulations from Re = 8000 to 25 000. The Reynolds number dependency of the mean torque changes near Re = 10 000, and the transition is closely linked to the turbulence characteristics. As the Reynolds number increases, the fine scale eddies are more densely populated and take more various tilting angles. The joint probability density function of the tilting angle and the radial position exhibits a preferential pattern corresponding to the large scale motion of Taylor vortices. The present results suggest that in this Reynolds number range, the fine scale eddies progressively prevail a large part of the domain, and their contribution to the fundamental statistics such as the Reynolds shear stress becomes more evident
The Arithmetic and Geometry of a Class of Algebraic Surfaces of General Type and Geometric Genus One
Full text linkWe study of a class of algebraic surfaces of general type and geometric genus one, with a view toward arithmetic results. These surfaces, called CC surfaces here, have been classified over the complex numbers by Catanese and Ciliberto. At the heart of our work is a large monodromy result for a family containing all members of a large subclass of CC surfaces, called the admissible CC surfaces. This result is obtained by an analysis of degenerations of admissible CC surfaces.
We apply this monodromy theorem to prove the Tate and semisimplicity conjectures for all admissible CC surfaces over finitely-generated fields of characteristic zero, which are statements about the Galois representations on their cohomology. We also apply the theorem to produce an example of an algebraic cycle on a Shimura variety of orthogonal type that is not contained in any proper special subvariety; this we do by using the period map of the aforementioned family. Finally, we deduce the existence of complex CC surfaces with the minimum possible Picard number.</p
On the Piatetski-Shapiro construction for integral models of Shimura varieties
Full text linkWe study the Piatetski-Shapiro construction, which takes a totally real field F and a Shimura datum (G,X) and produces a new Shimura datum (H,Y). If F is Galois, then the Galois group Gamma of F acts on (H,Y), and we show that the Gamma-fixed points of the Shimura varieties for (H,Y) recover the Shimura varieties for (G,X) under some hypotheses. For Shimura varieties of Hodge type with parahoric level, we show that the same is true for the p-adic integral models constructed by Pappas--Rapoport, if p is unramified in F. We also study the Gamma-fixed points of the Igusa stacks of Zhang for (H,Y) and prove optimal results
Ge1-x Sn (x) nanodots crystal nuclei for solid phase crystallization of poly-Si1-x-y Ge (x) Sn (y)
Full text linkEichler–Shimura isomorphism and group cohomology on arithmetic groups
Full text linkIn this article, we give a group cohomological interpretation to the Eichler–Shimura isomorphism. For any quaternion algebra A over a totally real field with multiplicative group G, we interpret a weight (k1,k2,⋯,kd)-automorphic form of G as a G(F)-invariant homomorphism of (G∞,K∞)-modules. Then the Eichler–Shimura isomorphism is given by the connection morphism provided by the natural exact sequences defining the (G∞,K∞)-module of discrete series of weight (k1,k2,⋯,kd). © 2017 Elsevier Inc
Ge1-x Sn (x) nanodots crystal nuclei for solid phase crystallization of poly-Si1-x-y Ge (x) Sn (y)
No full textThis work was supported by JSPS KAKENHI Grant No. 21K04137
On The Hecke Orbit Conjecture for PEL Type Shimura Varieties
Full text linkThe Hecke orbit conjecture plays an important role in understanding the geometric structure of Shimura varieties. First postulated by Chai and Oort in 1995, the Hecke orbit conjecture predicts that prime-to-p Hecke correspondences on mod p reductions of Shimura varieties characterize the foliation structure formed by Oort's central leaves. In other words, every prime-to-p Hecke orbit is Zariski dense in the central leaf containing it. Roughly speaking, a central leaf is the locus in a Shimura variety consisting of all points whose corresponding Barsotti-Tate groups belong to a fixed geometric isomorphism class. On the other hand, the prime-to-p Hecke orbit of a closed point x is the (countable) set consisting of all points y such that there is a prime-to-p quasi-isogeny from x to y.
In 2005, Chai and Yu proved the Hecke orbit conjecture for Hilbert modular varieties, followed by a proof for Siegel modular varieties by Chai and Oort in the same year. The major purpose of the present work is to generalize the method of Chai and Oort to Shimura varieties of PEL type. We show that the Hecke orbit conjecture holds for points in certain irreducible components of Newton strata under our assumptions.</p
On rigid analytic uniformizations of Jacobians of Shimura curves
No full textThe main goal of this article is to give an explicit rigid analytic uniformization of the maximal toric quotient of the Jacobian of a Shimura curve over Q at a prime dividing exactly the level. This result can be viewed as complementary to the classical theorem of Cerednik and Drinfeld which provides rigid analytic uniformizations at primes dividing the discriminant. As a corollary, we offer a proof of a conjecture formulated by M. Greenberg in his paper on Stark-Heegner points and quaternionic Shimura curves, thus making Greenberg's construction of local points on elliptic curves over Q unconditional.Peer ReviewedPostprint (author's final draft
- …
