Related papers: Miyawaki's $F_{12}$ Spinor L-function Conjecture

The Shimura correspondence is a fundamental tool in the study of half-integral weight modular forms. In this paper, we prove a Shimura-type correspondence for spaces of half-integral weight cusp forms which transform with a power of the…

In this note we improve on the results of our earlier paper[BLGG12], proving a near-optimal theorem on the existence of ordinary lifts of a mod l Hilbert modular form for any odd prime l.

In this paper we construct a two variables $p$-adic $L$-function for the standard representation associated with a Hida family of parallel weight genus $g$ Siegel forms, using a method previously developed by B\"ocherer--Schmidt in one…

We establish formulae for the Iwasawa invariants of Mazur--Tate elements of cuspidal eigenforms, generalizing known results in weight 2. Our first theorem deals with forms of "medium" weight, and our second deals with forms of small slope .…

In this paper, first we give a weak version of Ikeda's conjecture on the period of the Ikeda-Miyawaki lift. Next, we confirm this conjecture rigorously in some cases.

In this note we give a detailed construction of a $\Lambda$-adic $\mathfrak{d}$-th Shintani lifting. We derive a $\Lambda$-adic version of Kohnen's formula relating Fourier coefficients of half-integral weight modular forms and special…

This article studies the finite--slope analogue of Loeffler's conjectural framework for Rankin--Selberg $p$-adic $L$-functions in universal deformation families. Starting from residual representations $\bar\rho_1,\bar\rho_2$ of tame…

Let f be a cusp form for the group SL(3, Z) with Langlands parameter mu and associated L-function L(s, f). If mu is in generic position, i.e. away from the Weyl chamber walls and away from the self-dual forms, we prove the subconvexity…

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…

We give two global integrals that unfold to a non-unique model and represent the partial Spin $L$-function on $\mathrm{GSp}_6$. We deduce that for a wide class of cuspidal automorphic representations $\pi,$ the partial Spin $L$-function is…

We prove an upper bound for the fifth moment of Hecke L-functions associated to holomorphic Hecke cusp forms of full level and weight k in a dyadic interval K < k < 2K, as K tends to infinity. The bound is sharp on Selberg's eigenvalue…

We obtain pullback formulas for Klingen Eisenstein series with arbitrary levels, with respect to both Siegel congruence and paramodular subgroups, in degree two. Pullback results are used, along with the Fourier series expansion of Klingen…

Continuing the study of the Iwasawa theory of symmetric powers of CM modular forms at supersingular primes begun by the first author and Antonio Lei, we prove a Main Conjecture equating the "admissible" $p$-adic $L$-functions to…

Let k and n be positive even integers. For a cuspidal Hecke eigenform h in the Kohnen plus subspace of weight k-n/2+1/2 and level 4, let I(h) be the Duke-Imamoglu-Ikeda lift of h in the space of cusp forms of weight k for Sp(n,Z), and f the…

Let F be a Siegel cusp form of weight k and genus n>1 with Fourier-Jacobi coefficients f_m. In this article, we estimate the growth of the Petersson norms of f_m, where m runs over an arithmetic progression. This result sharpens a recent…

In this paper, we prove a converse theorem for half-integral weight modular forms assuming functional equations for $L$-series with additive twists. This result is an extension of Booker, Farmer, and Lee's result in [BFL22] to the…

Let $\pi$ be a Hecke-Maass cusp form for $SL(3,\mathbb Z)$. In this paper we will prove the following subconvex bound $$ L(\tfrac{1}{2}+it,\pi)\ll_{\pi,\varepsilon} (1+|t|)^{3/4-1/16+\varepsilon}. $$

The Kudla lift studied in this article is a classical version for Picard modular forms of the automorphic theta lift between $\text{GU}(2)$ and $\text{GU}(3)$. We construct an explicit $p$-adic analytic family of Picard modular forms…

We formulate analogues of the Birch and Swinnerton-Dyer conjecture for the $p$-adic $L$-functions of Bertolini-Darmon-Prasanna attached to elliptic curves $E/\mathbf{Q}$ at primes $p$ of good ordinary reduction. Using Iwasawa theory, we…

In this paper we improve the upper bound of the third order Hankel determinant for the class of Ozaki close-to-convex functions. The sharp bound is conjectured.