Related papers: Some remarks on strong multiplicity one for paramo…

We show that Galois theory of cyclotomic number fields provides a powerful tool to construct systematically integer-valued matrices commuting with the modular matrix S, as well as automorphisms of the fusion rules. Both of these…

"Thick" or "microformal" morphisms of supermanifolds generalize ordinary maps. They were discovered as a tool for homotopy algebras. Namely, the corresponding pullbacks provide $L_{\infty}$-morphisms for $S_{\infty}$ or Batalin--Vilkovisky…

We give a parametrization of the possible Serre invariants $(N,k,\nu)$ of modular mod $\ell$ Galois representations of the exceptional types $A_4$, $S_4$, $A_5$, in terms of local data attached to the fields cut out by the associated…

We prove a Voronoi formula for coefficients of a large class of $L$-functions including Maass cusp forms, Rankin-Selberg convolutions, and certain isobaric sums. Our proof is based on the functional equations of $L$-functions twisted by…

In this paper, we consider automorphic forms on $\mathrm{Sp}_4(\mathbb{A}_\mathbb{Q})$ which generate large discrete series representations of $\mathrm{Sp}_4(\mathbb{R})$ as $(\mathfrak{sp}_4(\mathbb{R}),K_\infty)$-modules. We determine the…

We prove new automorphy lifting theorems for residually reducible Galois representations of unitary type in which the residual representation is permitted to have an arbitrary number of irreducible constituents.

We propose an explicit and practical algorithm for computing Galois conjugates and irreducible polynomials for special values of modular functions evaluated at CM points associated with imaginary quadratic orders. Our approach builds upon…

This article is concerned with the Fourier coefficients of cusp forms (not necessarily eigenforms) of half-integer weight lying in the plus space. We give a soft proof that there are infinitely many fundamental discriminants $D$ such that…

We propose an improved algorithm for computing mod $\ell$ Galois representations associated to a cusp form $f$ of level one. The proposed method allows us to explicitly compute the case with $\ell=29$ and $f$ of weight $k=16$, and the cases…

In this paper we prove a Gross-Zagier type formula for the anticyclotomic p-adic L-function of an elliptic modular form f of higher weight and of multiplicative type at p. For such f we also decribe explicitely the local Galois…

We establish a relation between Galois reducibility and Endoscopy for genus 2 Siegel cusp forms which have rational eigenvalues and are unramified at 3

We give variants of lifting construction, which define new classes of modular forms on the Siegel upper half-space of complex dimension 3 with respect to the full paramodular groups (defining moduli of Abelian surfaces with arbitrary…

We studied framed deformations of two dimensional Galois representation of which the residue representation restrict to decomposition groups are scalars, and established a modular lifting theorem for certain cases. We then proved a family…

After Zagier proved that the traces of singular moduli $j(z)$ are Fourier coefficients of a weakly holomorphic modular form, various properties of the traces of the singular values of modular functions mostly on the full modular group…

We compute modular Galois representations associated with a newform $f$, and study the related problem of computing the coefficients of $f$ modulo a small prime $\ell$. To this end, we design a practical variant of the complex…

We propose three kinds of explicit formulas for the elliptic lambda function by the elliptic modular function. Further, we derive incredible cubic identities as a corollary of our explicit formulas and evaluate some singular values of the…

We construct $p$-adic $L$-functions associated with $p$-refined cohomological cuspidal Hilbert modular forms over any totally real field under a mild hypothesis. Our construction is canonical, varies naturally in $p$-adic families, and does…

We give a characterisation of the field into which quotients of values of L-functions associated to a cusp form belong. The construction involves shifted convolution series of divisor sums and to establish it we combine parts of F. Brown's…

We construct and analyze unfolded off-shell systems for chiral and vector supermultiplets using multispinor formalism and external currents. We find that auxiliary variables of multispinor formalism allow for the interesting reorganization…

The study of modular representation theory of the double covering groups of the symmetric and alternating groups reveals rich and subtle combinatorial and algebraic phenomena involving their irreducible characters and the structure of their…