Related papers: Slopes of modular forms and the ghost conjecture, …

We prove a version of the Extra-zero conjecture formulated by the first named author for p-adic L-functions associated to Rankin-Selberg convolutions of modular forms of the same weight. The novelty of this result is to provide strong…

We present a new method to analytically prove global stability in ghost-ridden dynamical systems. Our proposal encompasses all prior results and consequentially extends them. In particular, we show that stability can follow from a conserved…

Recent work has shown that non-local modifications of the Einstein equations can have interesting cosmological consequences and can provide a dynamical origin for dark energy, consistent with existing data. At first sight these theories are…

We state and verify up to weight 172 a conjecture on the existence of a certain generating set for spaces of classical Siegel modular forms. This conjecture is particularly useful for calculations involving Fourier expansions. Using this…

Sums of the singular series constants that appear in the Hardy--Littlewood $k$-tuples conjectures have long been studied in connection to the distribution of primes. We study constrained sums of singular series, where the sum is taken over…

The distance conjecture states that for theories with moduli coupled to gravity a tower of states becomes light exponentially in the geodesic distance in moduli space. This specifies how effective field theories break down for large field…

The Umbral Moonshine Conjectures assert that there are infinite-dimensional graded modules, for prescribed finite groups, whose McKay-Thompson series are certain distinguished mock modular forms. Gannon has proved this for the special case…

We state a conjecture, local Langlands in families, connecting the centre of the category of smooth representations on $\mathbb{Z}[\sqrt{q}^{-1}]$-modules of a quasi-split $p$-adic group $\mathrm{G}$ (where $q$ is the cardinality of the…

Fundamental conjectures in modular representation theory of finite groups, more precisely, Alperin's Weight Conjecture and Robinson's Ordinary Weight Conjecture, can be expressed in terms of fusion systems. We use fusion systems to connect…

We prove a natural analogue of the Sato-Tate conjecture for modular forms of weight 2 or 3 whose associated automorphic representations are a twist of the Steinberg representation at some finite place.

We prove a zig-zag conjecture describing the reductions of irreducible crystalline two-dimensional representations of $G_{{\mathbb{Q}}_p}$ of slope $\frac{3}{2}$ and exceptional weights. This along with previous works completes the…

Let F be a totally real field and p a rational prime unramified in F. We prove a partial classicality theorem for overconvergent Hilbert modular forms: when the slope is small compared to certain but not all weights, an overconvergent form…

A new representation is found for the action of the recently suggested ghost-free nonlocal gravity models generating de Sitter or Anti-de Sitter background with an arbitrary value of the effective cosmological constant. This representation…

In this paper we establish the correspondence between ghost-free bimetric theory and a class of higher derivative gravity actions, including conformal gravity and New Massive Gravity. We also characterize the relation between the respective…

We state conjectures that relate Hermitian modular forms of degree two and algebraic modular forms for the compact group $SO(6)$. We provide evidence for these conjectures in the form of dimension formulas and explicit computations of…

We prove that for forms of U(3) which are compact at infinity and split at places dividing a prime p, in generic situations the Serre weights of a mod p modular Galois representation which is irreducible when restricted to each…

Let F be a totally real field and p an odd prime. If r is a continuous, semisimple, totally odd mod p representation of the absolute Galois group of F which is tamely ramified at all places of F dividing p, then we formulate a conjecture…

In this article we will show how to compute $U_p$ acting on spaces of overconvergent $p$-adic modular forms when $X_0(p)$ has genus 1. We first give a construction of Banach bases for spaces of overconvergent $p$-adic modular forms, and…

The absolute sets of local systems on a smooth complex algebraic variety are the subject of a conjecture of N. Budur and B. Wang based on an analogy with special subvarieties of Shimura varieties. An absolute set should be the…

In theories with a hidden ghost sector that couples to visible matter through gravity only, empty space can decay into ghosts and ordinary matter by graviton exchange. Perturbatively, such processes can be very slow provided that the…