We show that there is a relationship between modular forms and totally odd multiple zeta values by relating the matrix EN,r, whose entries are given by the polynomial representations of the Ihara action, with even period polynomials. We also consider the matrix CN,r defined by Brown and give a new upper bound of the rank of CN,4. This result gives support to the uneven part of the motivic Broadhurst-Kreimer conjecture of depth 4.
In this paper, we show that n-dimensional (n ≥ 2) complete and non-compact smooth metric measure spaces with non-negative weighted Ricci curvature in which some Gagliardo-Nirenberg-type inequality holds are not far from the model metric measure n-space (i.e., the Euclidean metric n-space). Moreover, this fact, together with two generalized volume comparison theorems given in [P. Freitas et al. Calc. Var. Partial Differential Equations 51 (2014), 701-724], surprisingly leads to an interesting rigidity theorem for the given metric measure spaces.
We study the cones of q-ample divisors qAmp. In favourable cases, we identify a part where the closure qAmp and the nef cone have the same boundary. This is especially interesting for Fano (or almost Fano) varieties.
We prove the existence of global decaying solutions to the initial boundary value problem for the quasilinear wave equation of p-Laplacian type with Kelvin-Voigt dissipation and a derivative nonlinearity. To derive the required estimates of the solutions we employ a ‘loan’ method and a difference inequality for the energy.
We derive the asymptotic formula for the Fourier coefficients of the j-function using an arithmetic formula given by Kaneko based on Zagier's work on the traces of singular moduli. The key ingredient along with the Kaneko-Zagier formula is Laplace's method.
In this article, we define a projectively flat map of a compact Kähler manifold into the complex Grassmannian manifold, which is a kind of extension of a holomorphic map into the complex projective space. Then we show a rigidity theorem of a holomorphic isometric projectively flat immersion of Hermitian symmetric spaces of compact type. As an application, we classify holomorphic isometric projectively flat immersions of compact Kähler manifolds with parallel second fundamental form.
We consider two specific monodromy representations on the space of solutions of the generalized hypergeometric equation n+1En, which is satisfied by the generalized hypergeometric function n+1Fn. We express the matrix elements of the monodromy representations in each of the representations, determine a necessary and sufficient condition for each of the representations being irreducible, and give examples of subrepresentations when the representation is reducible.
We consider the Wiener sausage for a Brownian motion up to time t associated with a closed ball in even-dimensional cases. We obtain the asymptotic expansion of the expected volume of the Wiener sausage for large t. The result says that the expansion has many log terms, which do not appear in odd-dimensional cases.
We prove three theorems on finite real multiple zeta values: the symmetric formula, the sum formula and the height-one duality theorem. These are analogues of their counterparts on finite multiple zeta values.