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

We provide an alternative compact expression for the 11D pure spinor b-ghost by introducing a new set of negative ghost number operators made out of non-minimal pure spinor variables. Using the algebraic properties satisfied by these…

Generalized statistical models of voids and hierarchical structure in cosmology are developed. The often quoted negative binomial model and frequently used thermodynamic model are shown to be special cases of a more general distribution…

We propose a theoretically consistent modification of gravity in the infrared, which is compatible with all current experimental observations. This is an analog of Higgs mechanism in general relativity, and can be thought of as arising from…

Possible nonlinear completion of massive gravity is presented. An additional scalar ghost contained in linear theory condensates to give rise to positive-energy excitations.

Let $p$ be prime, $N$ be a positive integer prime to $p$, and $k$ be an integer. Let $P_k(t)$ be the characteristic series for Atkin's $U$ operator as an endomorphism of $p$-adic overconvergent modular forms of tame level $N$ and weight…

We show that noncongruence subgroups of SL_2(Z) projectively equivalent to congruence subgroups are ubiquitous. More precisely, they always exist if the congruence subgroup in question is a principal congruence subgroup Gamma(N) of level…

We explicitly show that general local higher-derivative theories with only complex conjugate ghosts and normal real particles are unitary at any perturbative order in the loop expansion. The proof presented here relies on integrating the…

Let $A$ be an abelian variety defined over a number field $F$ with supersingular reduction at all primes of $F$ above $p$. We establish an equivalence between the weak Leopoldt conjecture and the expected value of the corank of the…

We prove that all mod $p$ Hilbert modular forms arise via multiplication by generalized partial Hasse invariants from forms whose weight falls within a certain minimal cone. This answers a question posed by Andreatta and Goren, and…

In this semi-expository note, we give a new proof of a structure theorem due to Shimura for nearly holomorphic modular forms on the complex upper half plane. Roughly speaking, the theorem says that the space of all nearly holomorphic…

We present the theory of a supersymmetric ghost condensate coupled to N=1 supergravity. This is accomplished using a general formalism for constructing locally supersymmetric higher-derivative chiral superfield actions. The theory admits a…

Let $L/K$ be a finite Galois extension of number fields with Galois group $G$. Let $p$ be an odd prime and $r>1$ be an integer. Assuming a conjecture of Schneider, we formulate a conjecture that relates special values of equivariant Artin…

In this paper we show that Atkin and Swinnerton-Dyer type of congruences hold for weakly modular forms (modular forms that are permitted to have poles at cusps). Unlike the case of original congruences for cusp forms, these congruences are…

The study of linear perturbation theory for general functions of the Ricci and Gauss-Bonnet scalars is done over an empty anisotropic universe, i.e. the Kasner-type background, in order to show that an anisotropic background in general has…

We present a form convergence theorem for sequences of sectorial forms and their associated semigroups in a complex Hilbert space. Roughly speaking, the approximating forms $a_n$ are all `bounded below' by the limiting form $a$, but in…

We extend the mimetic cosmology to models containing gauge invariant $p$-forms. The $0$-form case reproduces the well-known results of the mimetic dark matter, the $1$-form corresponds to the gauge field mimetic model while the $2$-form…

We p-adically interpolate the relative de Rham cohomology of the universal elliptic curve over strict neighbourhoods of the ordinary locus of modular curves, together with the Hodge filtration and Gauss-Manin connection. Sections of these…

The aim of this paper is to prove the statement in the title. As a by-product, we obtain new globalization results in cases never considered before, such as partial corepresentations of Hopf algebras. Moreover, we show that for partial…

We prove the weight-monodromy conjecture for varieties which are p-adically uniformized by a product of the Drinfeld upper half spaces. It is an easy consequence of Dat's work on the cohomology complex of the Drinfeld upper half space.

We provide a geometric Hodge-Tate map giving generic description of the overconvergent modular symbols of some p-adic (accessible) weight k, base-changed to C_p, in terms of overconvergent modular forms of weight k+2.