We study sign changes and non-vanishing of a certain double sequence of Fourier coefficients of cusp forms of half-integral weight.
We study sign changes and non-vanishing of a certain double sequence of Fourier coefficients of cusp forms of half-integral weight.
Combining theorems of Voisin and Marian, Shen, Yin and Zhao, we compute the dimensions of the orbits under rational equivalence in the Mukai system of rank two and genus two. We produce several examples of algebraically coisotropic and constant cycle subvarieties.
We introduce a model for random chain complexes over a finite field. The randomness in our complex comes from choosing the entries in the matrices that represent the boundary maps uniformly over (mathbb {F}_q), conditioned on ensuring that the composition of consecutive boundary maps is the zero map. We then investigate the combinatorial and homological properties of this random chain complex.
In this paper, we consider a kind of area-preserving flow for closed convex planar curves which will decrease the length of the evolving curve and make the evolving curve more and more circular during the evolution process. And the final shape of the evolving curve will be a circle as time (trightarrow +infty ).
Let X be a smooth quintic hypersurface in (mathbb {P}^3), let C be a smooth hyperplane section of X, and let (H=mathcal {O}_X(C)). In this paper, we give a necessary and sufficient condition for the line bundle given by a non-zero effective divisor on X to be initialized and aCM with respect to H.
We study p-adic L-functions (L_p(s,chi )) for Dirichlet characters (chi ). We show that (L_p(s,chi )) has a Dirichlet series expansion for each regularization parameter c that is prime to p and the conductor of (chi ). The expansion is proved by transforming a known formula for p-adic L-functions and by controlling the limiting behavior. A finite number of Euler factors can be factored off in a natural manner from the p-adic Dirichlet series. We also provide an alternative proof of the expansion using p-adic measures and give an explicit formula for the values of the regularized Bernoulli distribution. The result is particularly simple for (c=2), where we obtain a Dirichlet series expansion that is similar to the complex case.
The moduli spaces of flat ({text{SL}}_2)- and ({text{PGL}}_2)-connections are known to be singular SYZ-mirror partners. We establish the equality of Hodge numbers of their intersection (stringy) cohomology. In rank two, this answers a question raised by Tamás Hausel in Remark 3.30 of “Global topology of the Hitchin system”.
We give generators and relations for the graded rings of Hermitian modular forms of degree two over the rings of integers in ({mathbb {Q}}(sqrt{-7})) and ({mathbb {Q}}(sqrt{-11})). In both cases we prove that the subrings of symmetric modular forms are generated by Maass lifts. The computation uses a reduction process against Borcherds products which also leads to a dimension formula for the spaces of modular forms.
We identify the p-adic unit roots of the zeta function of a projective hypersurface over a finite field of characteristic p as the eigenvalues of a product of special values of a certain matrix of p-adic series. That matrix is a product (F(varLambda ^p)^{-1}F(varLambda )), where the entries in the matrix (F(varLambda )) are A-hypergeometric series with integral coefficients and (F(varLambda )) is independent of p.
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