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We introduce techniques to analyze unitary operations in terms of quadratic form expansions, a form similar to a sum over paths in the computational basis when the phase contributed by each path is described by a quadratic form over…

We establish a quantitative version of Oppenheim's conjecture for generic ternary indefinite quadratic forms using an analytic number theory approach. The statements come with power gains and in some cases are essentially optimal

In this paper, we give a method to construct a classical modular form from a Hilbert modular form. By applying this method, we can get linear formulas which relate the Fourier coefficients of the Hilbert and classical modular forms. The…

We show that the restriction to square-free numbers of the representation function attached to a norm form does not correlate with nilsequences. By combining this result with previous work of Browning and the author, we obtain an…

This paper provides an unique dual representation of set-valued lower semi-continuous quasiconvex and convex functions. The results are based on a duality result for increasing set valued functions.

Taking the XXZ chain as the main example, we give a review of an algebraic representation of correlation functions in integrable spin chains obtained recently. We rewrite the previous formulas in a form which works equally well for the…

The recurrence matrix relations, differentiation formulas, and analytical and fractional integral properties of incomplete gamma matrix functions $\gamma(Q, x)$ and $\Gamma(Q, x)$ are all covered in this article. The generalized incomplete…

In this article, we extend the nonabelian Hodge correspondence in positive characteristic to the nonlinear setting.

We give a sufficient condition for the existence of a quadratic exponential vector with test function in L2(Rd) ? L?(Rd). We prove the linear independence and totality, in the quadratic Fock space, of these vectors. Using a technique…

This is a complete classification of the complex forms of quaternionic symmetric spaces

In this article, we study the invariant differential forms which a correspondence of curves admits. We also try to classify the correspondences of $\mathbb{P}^1$ that admits such invariant differential forms.

In this paper we examine the existence of bicomplexified inverse Fourier transform as an extension of its complexified inverse version within the region of convergence of bicomplex Fourier transform. In this paper we use the idempotent…

For suitable pairs of diagonal quadratic forms in 8 variables we use the circle method to investigate the density of simultaneous integer solutions and relate this to the problem of estimating linear correlations among sums of two squares.

We establish some identities of Euler related sums. By using these identities, we discuss the closed form representations of sums of harmonic numbers and reciprocal parametric binomial coefficients through parametric harmonic numbers,…

A correspondence between different $Pin$-type structures on a compact surface and quadratic (linear) forms on its homology is constructed. Addition of structures is defined and expressed in terms of these quadratic forms.

The paper explores various special functions which generalize the two-parametric Mittag-Leffler type function of two variables. Integral representations for these functions in different domains of variation of arguments for certain values…

A Lie superalgebra endowed with a supersymmetric, even, non-degenerate, invariant bilinear form is called a quadratic Lie superalgebra. In this paper we give inductive descriptions of quadratic Lie superalgebras in terms of generalized…

In this paper we introduce and investigate the notions of diagrams and discrete extensions in the study of finitary $2$-representations of finitary $2$-categories.

We show how to calculate correlation functions of two matrix models. Our method consists in making full use of the integrable hierarchies and their reductions, which were shown in previous papers to naturally appear in multi--matrix models.…

In this paper, we mainly investigate profound interconnections between combinatorial designs, linear codes, and Boolean functions.