Related papers: Twisting of Siegel paramodular forms

We compute the space $S_2(K(N))$ of weight $2$ Siegel paramodular cusp forms of squarefree level $N<300$. In conformance with the paramodular conjecture of A. Brumer and K. Kramer, the space is only the additive (Gritsenko) lift space of…

The mapping of topologically nontrivial gauge transformations in noncommutative gauge theory to corresponding commutative ones is investigated via the operator form of the Seiberg-Witten map. The role of the gauge transformation part of the…

Noncommutative geometry provides both a unified description of the Standard Model of particle physics together with Einstein-Hilbert action (in euclidean signature) and some tools to go beyond the Standard Model. In this paper, we extend to…

We give a pedagogical account of noncommutative gauge and gravity theories, where the exterior product between forms is deformed into a $\star$-product via an abelian twist (e.g. the Groenewold-Moyal twist). The Seiberg-Witten map between…

We classify Siegel modular cusp forms of weight two for the paramodular group K(p) for primes p< 600. We find that weight two Hecke eigenforms beyond the Gritsenko lifts correspond to certain abelian varieties defined over the rationals of…

Let $\pi$ be a $SL(3,\mathbb{Z})$ Hecke Maass-cusp form, $f$ be a $SL(2,\mathbb{Z})$ holomorphic cusp form or Maass-cusp form with normalized Fourier coefficients $\lambda_{\pi}(r,n) \text{ and }\lambda_{f}(n)$ respectively and $\chi$ be…

Let $k \geq 2$ and $N$ be positive integers and let $\chi$ be a Dirichlet character modulo $N$. Let $f(z)$ be a modular form in $M_k(\Gamma_0(N),\chi)$. Then we have a unique decomposition $f(z)=E_f(z)+S_f(z)$, where $E_f(z) \in…

Starting with a primitive Dirichlet character of conductor $N$, we construct a paramodular Siegel Eisenstein series of level $N^2$ and weight $k\geq4$. We calculate the Fourier expansion of the holomorphic Siegel modular form thus…

Noncommutative versions of theories with a gauge freedom define (when they exist) consistent deformations of their commutative counterparts. General aspects of Seiberg-Witten maps are discussed from this point of view. In particular, the…

The Seiberg-Witten map links noncommutative gauge theories to ordinary gauge theories, and allows to express the noncommutative variables in terms of the commutative ones. Its explicit form can be found order by order in the noncommutative…

We twist Zagier's function $f_{k,D}$ by a sign function and a genus character. Assuming weight $0 < k \equiv 2 \pmod{4}$, and letting $D$ be a positive non-square discriminant, we prove that the obstruction to modularity caused by the sign…

Let f be a Hecke-Maass or holomorphic primitive cusp form for $SL(2,\mathbb{Z})$ with Fourier coefficients $\lambda_{f}(n)$. Let $\chi$ be a primitive Dirichlet character of modulus p, where p is a prime number. In this article we prove the…

The Neumann--Zagier matrices of an ideal triangulation are integer matrices with symplectic properties whose entries encode the number of tetrahedra that wind around each edge of the triangulation. They can be used as input data for the…

We provide a purely local computation of the (elliptic) twisted (by "transpose-inverse") character of the representation \pi=I(\1) of PGL(3) over a p-adic field induced from the trivial representation of the maximal parabolic subgroup. This…

In the 1980s B\"ocherer formulated a conjecture relating the central values of the imaginary quadratic twists of the spin L-function attached to a Siegel modular form $F$ to the Fourier coefficients of $F$. This conjecture has been proved…

We introduce an infinite family of Kronecker series twisted by characters. As an application, we give a closed formula for the sum of all Hecke eigenforms on ${\Gamma}_0(N) $ multiplied by their twisted period polynomials in terms of the…

Let $f$ and $f'$ be genus $2$ cuspidal Siegel paramodular newforms. We prove that if their Hecke eigenvalues $a_p$ and $a_p'$ satisfy a non-trivial polynomial relation $P(a_p, a_p') = 0$ for a set of primes $p$ of positive density, then $f$…

The possibility of noncommutative topological gravity arising in the same manner as Yang-Mills theory is explored. We use the Seiberg-Witten map to construct such a theory based on a SL(2,C) complex connection, from which the Euler…

We construct isomorphisms between spaces of vector-valued modular forms for the dual Weil representation and certain spaces of scalar-valued modular forms in the case that the underlying finite quadratic module $A$ has order $p$ or $2p$,…

Let $q \in \mathbb{Z} [i]$ be prime and $\chi $ be the primitive quadratic Hecke character modulo $q$. Let $\pi$ be a self-dual Hecke automorphic cusp form for $\mathrm{SL}_3 (\mathbb{Z} [i] )$ and $f$ be a Hecke cusp form for $\Gamma_0 (q)…