Related papers: Lehmer's type congruences for lacunary harmonic su…

Direct links between generalized harmonic numbers, linear Euler sums and Tornheim double series are established in a more perspicuous manner than is found in existing literature. We show that every linear Euler sum can be decomposed into a…

The theory of quaternionic modular forms has been studied for decades as an example of the modular forms of many variables. The purpose of this study is to provide some congruence relations satisfied by such quaternionic modular forms.

Characterizations for Riemannian submersions to be harmonic or biharmonic are shown. Examples of biharmonic but not harmonic Riemannian submersions are shown.

We prove and generalize some recent conjectures of Z.-W. Sun on infinite series whose summands involve products of harmonic numbers and several binomial coefficients. We evaluate various classes of infinite sums in closed form by…

Recently we introduced a new class of relations for Bernoulli symmetric polynomials. This manuscript shows that these relations are valid for arbitrary homogeneous symmetric polynomial. Analysis of these relations leads to the discovery of…

In this paper, we consider transversally harmonic maps between Riemannian manifolds with Riemannian foliations. In terms of the Bochner techniques and sub-Laplacian comparison theorem, we are able to establish a generalization of the…

We prove several congruences for trinomial coefficients.

We develop a canonical form for congruence of max plus symmetric matrices. We use the same canonical form to get results in the generalized eigenvector problem. We have also utilized the canonical form to find all symmetric matrices that…

Complex manifolds with compatible metric have a naturally defined subspace of harmonic differential forms that satisfy Serre, Hodge, and conjugation duality, as well as hard Lefschetz duality. This last property follows from a…

Dimer models are a combinatorial tool to describe certain algebras that appear as noncommutative crepant resolutions of toric Gorenstein singularities. Unfortunately, not every dimer model gives rise to a noncommutative crepant resolution.…

We give a simplified presentation of some results about recurrences of certain sequences of binomial sums in terms of (generalized) Fibonacci and Lucas polynomials.

We establish some Schwarz type Lemmas for mappings defined on the unit disk with bounded Laplacian. Then we apply these results to obtain boundary versions of the Schwarz lemma.

We prove an isomorphism of Floer cohomologies under geometric composition of Lagrangian correspondences in exact and monotone settings.

We give congruences between the Eisenstein series and a cusp form in the cases of Siegel modular forms and Hermitian modular forms. We should emphasize that there is a relation between the existence of a prime dividing the $k-1$-th…

We study analogues of classical inequalities for the eigenvalues of sums of pseudo-Hermitian matrices.

Following the paper "Note on theta series for Niemeier lattices", we study some congruence properties satisfied by the theta series associated with Niemeier lattices.

In this paper, we discuss the associated family of harmonic maps $\mathcal{F}: M \rightarrow G/K$ from a Riemann surface $M$ into inner symmetric spaces of compact or non-compact type which are either algebraic or totally symmetric. These…

The aim of the present paper is to investigate new types of recurrence in Finsler geometry, namely, hyper-generalized recurrence and generalized conharmonic recurrence. The properties of such recurrences and their relations to other Finsler…

In this paper, we establish the curvature estimates for a class of Hessian type equations. Some applications are also discussed.

We prove that a tolerance relation of a lattice is a homomorphic image of a congruence relation.