Related papers: Factorisation of two-variable p-adic L-functions

Let $f$ be an entire function and $L(f)$ a linear differential polynomial in $f$ with constant coefficients. Suppose that $f$, $f'$, and $L(f)$ share a meromorphic function $\alpha(z)$ that is a small function with respect to $f$. A…

We give a criterion in terms of p-adic Asai L-functions for a cuspidal automorphic representation of GL(2) over a real quadratic field to be a distinguished representation, providing a p-adic counterpart of a well-known theorem of Flicker…

In the previous paper we generalized Greenberg's construction of the $\Cal L$-invariant to semistable representations. Here we prove that this construction is compatible with Perrin-Riou's theory of $p$-adic $L$-functions

Two decades ago P. Martin and D. Woodcock made a surprising and prophetic link between statistical mechanics and representation theory. They observed that the decomposition numbers of the blob algebra (that appeared in the context of…

Let $K$ be an imaginary quadratic field. In this article, we study the eigenvariety for $\mathrm{GL}_2/K$, proving an \'etaleness result for the weight map at non-critical classical points and a smoothness result at base-change classical…

We establish power-saving estimates for general bilinear forms with Kloosterman sums modulo arbitrary q, including when both variables are shorter than the Polya-Vinogradov range. As an application, we obtain power-saving asymptotics for…

We show that if F is a totally real field in which p splits completely and f is a mod p Hilbert modular form with parallel weight 2<k<p, which is totally ordinary at p and has tamely ramified Galois representation at all primes dividing p,…

We introduce an analog of part of the Langlands-Shahidi method to the p-adic setting, constructing reciprocals of certain p-adic L-functions using the nonconstant terms of the Fourier expansions of Eisenstein series. We carry out the method…

Let $E$ be an elliptic curve---defined over a number field $K$---without complex multiplication and with good ordinary reduction at all the primes above a rational prime $p \geq 5$. We construct a pairing on the dual $p^\infty$-Selmer group…

We define "sliding functors", which are exact endofunctors of the category of multi-graded modules over a polynomial ring. They preserve several invariants of modules, especially the (usual) depth and Stanley depth. In a similar way, we can…

Let f be a modular eigenform of even weight k>0 and new at a prime p dividing exactly the level, with respect to an indefinite quaternion algebra. The theory of Fontaine-Mazur allows to attach to f a monodromy module D_FM(f) and an…

The explicit formulas of operations, in particular addition and multiplication, of $p $-adic integers are presented. As applications of the results, at first the explicit formulas of operations of Witt vectors with coefficients in…

Inspired by several alternative definitions of continued fraction expansions for elements in $\mathbb Q_p$, we study $p$-adically convergent periodic continued fractions with partial quotients in $\mathbb Z[1/p]$. To this end, following a…

We define an axiomatic class of L-functions extending the Selberg class. We show in particular that one can recast the traditional conditions of an Euler product, analytic continuation and functional equation in terms of distributional…

We give a new proof of a conjecture of Darmon, Lauder and Rotger regarding the computation of the $\mathcal L$-invariant of the adjoint of a weight one modular form in terms of units and $p$-units. While in our previous work with Rotger the…

We introduce a geometric formalism for studying modular forms of half-integral weight and explore some of its basic properties. Geometric Hecke operators are constructed and some basic spaces of $p$-adic forms are introduced. The $p$-adic…

We consider the task of approximating a matrix function $f(A)$, where $A$ is a matrix in which only a relatively small number of (not necessarily consecutive) sub- and superdiagonals contain nonzero entries. Approximating $f$ by a…

Let $\k$ be a global function field in 1-variable over a finite extension of $\Fp$, $p$ prime, $\infty$ a fixed place of $\k$, and $\A$ the ring of functions of $\k$ regular outside of $\infty$. Let $E$ be a Drinfeld module or $T$-module.…

A classification is provided of functors, in particular polynomial ones, from a category with a zero object in which every object is a finite sum of copies of a generating object, into an abelian category. This classification is extended to…

We generalize recent matrix-based factorization theorems for Lambert series generating functions generating the coefficients $(f \ast 1)(n)$ for some arithmetic function $f$. Our new factorization theorems provide analogs to these…