Related papers: Slice monogenic theta series

This paper develops a generalized cotangent-type series, extending classical expansions to higher-order lattice sums. By introducing a new family of series indexed by integer powers, we derive closed form representations that combine…

This paper explores generalized slice monogenic functions by introducing their operator symbols, representation formula, and integral formula. The study extends the Teodorescu transform to a broader class of theorems and inferences,…

A systematic procedure for generating cubic multisections of Eisenstein series is given. The relevant series are determined from Fourier expansions for Eisenstein series by restricting the congruence class of the summation index modulo…

We introduce and study a family of power series, which we call Theta series, whose coefficients are in the tensor square of a quantum loop algebra. They arise from a coproduct factorization of the T-series of Frenkel--Hernandez, which are…

A poly-log time method to compute the truncated theta function, its derivatives, and integrals is presented. The method is elementary, rigorous, explicit, and suited for computer implementation. We repeatedly apply the Poisson summation…

We generalize the standard Poisson summation formula for lattices so that it operates on the level of theta series, allowing us to introduce noninteger dimension parameters (using the dimensionally continued Fourier transform). When…

Properties of four quintic theta functions are developed in parallel with those of the classical Jacobi null theta functions. The quintic theta functions are shown to satisfy analogues of Jacobi's quartic theta function identity and…

The two function theories of monogenic and of slice monogenic functions have been extensively studied in the literature and were developed independently; the relations between them, e.g. via Fueter mapping and Radon transform, have been…

In this Ph.D. dissertation (2018, Emory University) we prove theorems at the intersection of the additive and multiplicative branches of number theory, bringing together ideas from partition theory, $q$-series, algebra, modular forms and…

The Dedekind eta function $\eta(\tau)$ is defined by \[\eta(\tau)=e^{\pi i\tau/12}\prod_{n=1}^{\infty}\left(1-e^{2\pi i n\tau}\right),\quad\text{when}\;\text{Im}\,\tau>0.\] It plays an important role in number theory, especially in the…

In a recent paper, we introduced the concept of generalized partial-slice monogenic functions. The class of these functions includes both the theory of monogenic functions and of slice monogenic functions with values in a Clifford algebra.…

Recently the construction of various integral transforms for slice monogenic functions has gained a lot of attention. In line with these developments, the article at hand introduces the slice Fourier transform. In the first part, the kernel…

In this paper, we establish Kronecker limit type formulas for the generalized Mordell--Tornheim zeta function $\Theta(r,s,t,x)$ as a function of the third variable, in terms of Riemann-zeta and Gamma values. We also give series evaluations…

To obtain the Dirichlet series for complex powers of the Riemann zeta function, we define and study the basic properties of a sequence of polynomials that, used as coefficients of the respective terms of the Dirichlet series of the Riemann…

In a recent paper [Trans. Amer. Math. Soc. 378 (2025), 851-883], the concept of generalized partial-slice monogenic (or regular) function was introduced over Clifford algebras. The present paper shall extend the study of generalized…

Very recently, the concept of generalized partial-slice monogenic (or regular) functions has been introduced to unify the theory of monogenic functions and of slice monogenic functions over Clifford algebras. Inspired by the work of A.…

In this short paper, we find the transformation formula for the theta series under the action of the Jacobi modular group on the Siegel-Jacobi space. This formula generalizes the formula (5.1) obtained by Mumford in his book[p.189, Tata…

In this paper, we establish Kronecker limit type formulas for the Mordell-Tornheim zeta function $\Theta(r,s,t,x)$ as a function of the second as well as the third arguments. As an application of these formulas, we obtain results of…

We propose a generalization of the classical theta function to higher cohomology of the polarization line bundle on a family of complex tori with positive index. The constructed cocycles vary horizontally with respect to the (projective)…

In this paper, we consider the decomposition of theta series for lattice cosets of ternary lattices. We show that the natural decomposition into an Eisenstein series, a unary theta function, and a cuspidal form which is orthogonal to unary…