Related papers: Equidistribution theorems for holomorphic Siegel m…

In this paper, we associate Galois representations to globally generic cuspidal automorphic representations on GSp(4), over a totally real field F, which are Steinberg at some finite place. This association is compatible with the local…

We consider quantum symmetric algebras, FRT bialgebras and, more generally, intertwining algebras for pairs of Hecke symmetries which represent quantum hom-spaces. The paper makes an attempt to investigate Koszulness and Gorensteinness of…

In this paper we outline the Hecke theory for Hermitian modular forms in the sense of Hel Braun for arbitrary class number of the attached imaginary-quadratic number field. The Hecke algebra turns out to be commutative. Its inert part has a…

We equip the type $A$ diagrammatic Hecke category with a special derivation, so that after specialization to characteristic $p$ it becomes a $p$-dg category. We prove that the defining relations of the Hecke algebra are satisfied in the…

This work represents a systematic computational study of the distribution of the Fourier coefficients of cuspidal Hecke eigenforms of level $\Gamma_0(4)$ and half-integral weights. Based on substantial calculations, the question is raised…

We work out instances of a general conjecture on congruences between Hecke eigenvalues of induced and cuspidal automorphic representations of a reductive group, modulo divisors of certain critical L-values, in the case that the group is a…

Let F be a number field with adele ring A_F, and \pi an isobaric, algebraic automorphic representation of GL_4(A_F) of a fixed archimedean weight, which is quasi-regular, meaning that at every archimedean place v of F, the 4-dimensional…

We study moduli stabilization in 4D effective field theories with Sp(4,$\mathbb{Z}$) self-duality inspired by heterotic orbifold compactifications with Wilson lines. The target-space duality group of these theories is enhanced from…

We prove a new upper bound for the $L^4$-norm of a holomorphic Hecke newform of large fixed weight and prime level $q\to \infty$. This is achieved by proving a sharp mean value estimate for a related $L$-function on GL(6)

Let $G$ be a semisimple Lie group without compact factor and $\Gamma < G$ a torsion-free, cocompact, irreducible lattice. According to Selberg, periodic orbits of regular Weyl chamber flows live on maximal flat periodic tori of the space of…

Let $S_k(N)$ denote the space of cusp forms of even integer weight $k$ and level $N$. We prove an asymptotic for the Petersson trace formula for $S_k(N)$ under an appropriate condition. Using the non-vanishing of a Kloosterman sum involved…

Let $f$ be a cuspidal Hecke eigenform of level 1. We prove the automorphy of the symmetric power lifting $\mathrm{Sym}^n f$ for every $n \geq 1$. We establish the same result for a more general class of cuspidal Hecke eigenforms, including…

Let $F$ be an $L^2$-normalized Siegel cusp form for $\mathrm{Sp}_4(\mathbb{Z})$ of weight $k$ that is a Hecke eigenform and not a Saito--Kurokawa lift. Assuming the Generalized Riemann Hypothesis, we prove that its Fourier coefficients…

We extend the computations in [AGM1, AGM2, AGM3] to find the cohomology in degree five of a congruence subgroup Gamma of SL(4,Z) with coefficients in a field K, twisted by a nebentype character eta, along with the action of the Hecke…

In a letter to Tate, Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions on an adelic double coset space constructed from the endomorphism algebra of…

In this paper a theory of Hecke operators for higher order modular forms is established. The definition of cusp forms and attached L-functions is extended beyond the realm of parabolic invariants. The role of representation theoretic…

Given a continuous, odd, reducible and semi-simple $2$-dimensional representation $\bar\rho_0$ of $G_{\mathbb{Q},Np}$ over a finite field of odd characteristic $p$, we study the relation between the universal deformation ring of the…

Let $F$ be a totally real number field. We prove that a character of the spherical Hecke algebra appearing in the completed cohomology of Hilbert modular varieties is modular if the associated Galois representation is absolutely…

Let $K/\mathbb{Q}_p$ be a finite extension with residue field $k$. By a work of Emerton--Gee, irreducible components inside the reduced special fiber of the moduli stack of rank $n$ \'etale $(\varphi,\Gamma)$-modules are labeled by Serre…

Let $(\lambda_f(n))_{n\geqslant1}$ be the Hecke eigenvalues of a holomorphic cusp form $f$. We prove that the exponent of distribution of $\lambda_f*1$ in arithmetic progressions is as large as $\frac{1}{2}+\frac{1}{46}$ when the modulus…