Related papers: Non-cuspidal Bianchi modular forms and Katz $p$-ad…

The object of this article is to construct certain classes of arithmetically significant, holomorphic Siegel cusp forms F of genus 2, which are neither of Saito-Kurokawa type, in which case the degree 4 spinor L-function L(s, F) is…

Working in the p-adic analog of the complex numbers, we'll define a line integral on a small arc of a circle. This allows new versions of the Residue Theorem, the Cauchy-Goursat Theorem on discs with and without holes, Cauchy's Integral…

We construct four-variable $p$-adic $L$-functions for cuspidal Hida families on ${\rm GSp}(4)\times{\rm GL}(2)$ and prove a complete interpolation formula. The archimedean zeta integrals are computed by using a partial interpolation formula…

In this paper, we consider the relation between two nonabelian Fourier transforms. The first one is defined in terms of the Langlands-Kazhdan-Lusztig parameters for unipotent elliptic representations of a split p-adic group and the second…

We relate non-critical special values $p$-adic $L$-functions associated to algebraic Hecke characters of an imaginary quadratic number field with class number one to $p$-adic Coleman function called the $p$-adic Eisenstein-Kronecker series,…

We study $p$-adic families of cohomological automorphic forms for ${\mathrm{GL}}(2)$ over imaginary quadratic fields and prove that families interpolating a Zariski-dense set of classical cuspidal automorphic forms only occur under very…

Using an explicit Eichler-Shimura-Harder isomorphism, we establish the analogue of Manin's rationality theorem for Bianchi periods and hence special values of $L$-functions of Bianchi cusp forms. This gives a new short proof of a result of…

Analytic continuation and functional equation of a Dirichlet series constructed from two (not necessarily cuspidal) holomorphic modular forms is discussed, where either weights of the modular forms or characters are not necessarily equal to…

Two-dimensional $\sigma$-models corresponding to coset CFTs of the type $ (\hat{\mathfrak{g}}_k\oplus \hat{\mathfrak{h}}_\ell )/ \hat{\mathfrak{h}}_{k+\ell}$ admit a zoom-in limit involving sending one of the levels, say $\ell$, to…

In this paper, we study quadratic forms in spaces of holomorphic cusp forms. We show, conditionally, that when two quadratic forms in Hecke eigenforms share no common diagonal terms, their inner product is expected to converge to the sum of…

The isometric universality of the spaces $C(K)$ for $K$ a non scattered Hausdorff compact does not take into account the ``quality'' of the representation. Indeed, the existence of an isometric copy of a separable Banach space $X$ into…

In a groundbreaking paper, T. Fukaya and K. Kato proved a slight weakening of a conjecture of the author's relating modular symbols and cup products of cyclotomic units under an assumption that a Kubota-Leopoldt p-adic L-function has no…

Let G be a unitary, symplectic or special orthogonal group over a locally compact non-archimedean local field of odd residual characteristic. We construct many new supercuspidal representations of G, and Bushnell-Kutzko types for these…

In this work, we set up a theory of p-adic modular forms over Shimura curves over totally real fields which allows us to consider also non-integral weights. In particular, we define an analogue of the sheaves of k-th invariant differentials…

We define L-functions for meromorphic modular forms that are regular at cusps, and use them to: (i) find new relationships between Hurwitz class numbers and traces of singular moduli, (ii) establish predictions from the physics of…

With respect to the analytic-algebraic dichotomy, the theory of Siegel modular forms of half-integral weight is lopsided; the analytic theory is strong whereas the algebraic lags behind. In this paper, we capitalise on this to establish the…

We prove a formula for the Bloch-Kato logarithm of the bottom class in the Asai-Flach Euler system associated to a quadratic Hilbert modular form. We show that this can be expressed as a value, outside the interpolation range, of the p-adic…

The aim of this paper is to provide an analogue of the Ball-Rivoal theorem for $p$-adic $L$-values of Dirichlet characters. More precisely, we prove for a Dirichlet character $\chi$ and a number field $K$ the formula…

In this brief note, we consider p-adic unit roots or poles of L-functions of exponential sums defined over finite fields. In particular, we look at the number of unit roots or poles, and a congruence relation on the units. This raises a…

We construct the two-variable $p$-adic $q$-$L$-function which interpolates the generalized $q$-Bernoulli polynomials associated with primitive Dirichlet character $\chi$. Indeed, this function is the $q$-extension of two-variable $p$-adic…