Related papers: On Selmer groups and factoring $p$-adic $L$-functi…

We extend Kobayashi's formulation of Iwasawa theory for elliptic curves at supersingular primes to include the case $a_p \neq 0$, where $a_p$ is the trace of Frobenius. To do this, we algebraically construct $p$-adic $L$-functions…

We develop the local theory of the generalized doubling method for the $m$-fold central extension $Sp_{2n}^{(m)}$ of Matsumoto of the symplectic group. We define local $\gamma$-, $L$- and $\epsilon$-factors for pairs of genuine…

Following Ribet's seminal 1976 paper there have been many results employing congruences between stable cuspforms and lifted forms to construct non-split extensions of Galois representations. We show how this strategy can be extended to…

Let $k > 3$ be an integer and $p$ a prime with $p > 2k-2$. Let $f$ be a newform of weight $2k-2$ and level 1 so that $f$ is ordinary at $p$ and $\bar{\rho}_{f}$ is irreducible. Under some additional hypotheses we prove that…

In this paper, we prove Deligne's conjecture on the algebraicity of critical values of symmetric power $L$-functions associated to modular forms of weight greater than four. We also prove new cases of Blasius' conjecture on the algebraicity…

Let f be a cuspidal newform with complex multiplication (CM) and let p be an odd prime at which f is non-ordinary. We construct admissible p-adic L-functions for the symmetric powers of f, thus verifying general conjectures of Dabrowski and…

In this note we introduce zeta functions and L-functions for discrete and faithful representations of surface groups in PSL(d, R), for d >= 3. These are natural generalizations of the wellknown classical Selberg zeta function and L-function…

We construct $p$-adic $L$-functions interpolating the critical values of the degree eight $L$-functions of ${\rm GSp}(4)\times {\rm GL}(2)$ for cuspidal automorphic representations generated by $p$-ordinary Siegel modular forms of genus two…

Let G be the unramified unitary group in three variables defined over a p-adic field of odd residual characteristic. In this paper, we establish a theory of newforms for the Rankin-Selberg integral for G introduced by Gelbart and…

We prove that regular supercuspidal representations of $p$-adic groups are uniquely determined by their character values on very regular elements -- a special class of regular semisimple elements on which character formulae are very simple…

Our main objective in the present paper is to generalise the work of Blanco-Chac\'{o}n and Fornea on the $p$-adic Gross-Zagier formula for twisted triple product $p$-aidc $L$-function. We extend their main result to the case of finite slope…

Given a prime $p$, the $p$-adic Littlewood Conjecture stands as a well-known arithmetic variant of the celebrated Littlewood Conjecture in Diophantine Approximation. In the same way as the latter, it admits a natural function field analogue…

The p-parity conjecture for twists of elliptic curves relates multiplicities of Artin representations in p-infinity Selmer groups to root numbers. In this paper we prove this conjecture for a class of such twists. For example, if E/Q is…

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 construct the p-adic zeta function for a one-dimensional (as a p-adic Lie extension) non-commutative p-extension of a totally real number field such that the finite part of its Galois group is a pgroup with exponent p. We first calculate…

The purpose of this semi-expository article is to give another proof of a classical theorem of Shimura on the critical values of the standard L-function attached to a Hilbert modular form. Our proof is along the lines of previous work of…

We study the distribution of values of automorphic $L$-functions in a family of holomorphic cusp forms with prime level. We prove an asymptotic formula for a certain density function closely related to this value-distribution. The formula…

Let $K/F$ be a quadratic extension of p-adic fields. The Bernstein-Zelevinsky's classification asserts that generic representations are parabolically induced from quasi-square-integrable representations. We show, following a method…

Let $f$ be a newform of even weight $2\kappa$ for $D^\times$, where $D$ is a possibly split indefinite quaternion algebra over $\mathbb{Q}$. Let $K$ be a quadratic imaginary field splitting $D$ and $p$ an odd prime split in $K$. We extend…

Let $G$ be a $p$-adic reductive group. We determine the extensions between admissible smooth mod $p$ representations of $G$ parabolically induced from supersingular representations of Levi subgroups of $G$, in terms of extensions between…