Related papers: D\'{e}veloppements limit\'{e}s et r\'{e}version de…
The generating series associated to a certain sequence of limited Taylor expansions coincides with the continuously iterated Invert Transform and displays thus a nice functional equality.
In this note we produce examples of converging sequences of Galois representations, and study some of their properties. Some of the results here are used in the preprint math.NT/0210296.
We study the extension estimates for paraboloids in d-dimensional vector spaces over finite fields F_q with q elements. We use the connection between L^2 based restriction estimates and L^p\to L^r extension estimates for paraboloids. As a…
Generalizing the work of A. Morra and the authors, we give explicit formulas for the Dirichlet series generating function of $D_{\ell}$-extensions of odd prime degree $\ell$ with given quadratic resolvent. Over the course of our proof, we…
We show that the Drinfeld modular forms with $A$-expansion that have been constructed by the author are precisely the hyperderivatives of the subfamily of single-cuspidal Drinfeld modular forms with $A$-expansions that remain modular after…
In preparing the paper "Some extensions of Hilbert-Kunz multiplicity", we had occasion to perform an intricate set of computations pertaining to a single illustrative example. In the end, we have decided not to include the computations in…
We present inequalities and some applications to Kellers' limit and Carlemans' inequality.
In this note we provide a new, algebraic proof of the excessive Laurent phenomenon for mutations of potentials (in the sense of [Galkin S., Usnich A., Preprint IPMU 10-0100, 2010]) by introducing to this theory the analogue of the upper…
We study Hankel transforms of sequences, where the transform elements are members of the set {-1,0,1}. We relate these Hankel transforms to special continued fraction expansions. In particular, we posit a conjecture relating the…
We give a transform of convergent trigonometric series into equivalent convergent series and sufficient conditions for the transformed series to converge faster than the original one.
Under the generalized Lindel\"of Hypothesis in the t- and q-aspects, we bound exponential sums with coefficients of Dirichlet series belonging to a certain class. We use these estimates to establish a conditional result on squares of Hecke…
In this paper, the Hankel transform of the generalized q-exponential polynomial of the first form (q, r)-Whitney numbers of the second kind is established using the method of Cigler. Consequently, the Hankel transform of the first form (q,…
In this note, we obtain a quantitative improvement on the hypergraph variant of the Balog-Szemer\'{e}di-Gowers theorem due to Sudakov, Szemer\'{e}di, and Vu [Duke Math. J.129.1 (2005): 129--155]. Additionally, we prove the hypergraph…
In the present paper, we establish that Riesz transforms for Dunkl Hermite expansion as introduced in [4] are singular integral operators with H\"ormander's type conditions and we show that are bounded on $L^p(\mathbb{R}^d; d\mu_k) 1 < p <…
This is a revised version of the preprint which has been available electronically for a while. The paper will now appear in J. Ramanujan Math. Soc.
We define, and obtain the meromorphic continuation of, shifted Rankin-Selberg convolutions in one and two variables. As sample applications, this continuation is used to obtain estimates for single and double shifted sums and a Burgess-type…
We extend to multilinear Hankel operators the fact that some truncations of bounded Hankel operators are bounded. We prove and use a continuity property of bilinear Hilbert transforms on products of Lipschitz spaces and Hardy spaces.
The second named author previously constructed a functor $\mathbb{V}^\vee\circ D^\vee_\Delta$ from the category of smooth $p$-power torsion representations of $\mathrm{GL}_n(\mathbb{Q}_p)$ to the category of inductive limits of continuous…
We study an extension to Fourier transforms of the old problem on absolute convergence of the re-expansion in the sine (cosine) Fourier series of an absolutely convergent cosine (sine) Fourier series. The results are obtained by revealing…
Inspired by a recent work of D. Wei--S. Zhu on the extension of closed complex differential forms and Voisin's usage of the $\partial\bar{\partial}$-lemma, we obtain several new theorems of deformation invariance of Hodge numbers and…