Related papers: Twists of Hooley's $\Delta$-function over number f…

For characters of a non-Archimedean local field we have explicit formula for epsilon factors. But in general, we do not have any generalized twisting formula of epsilon factors. In this paper we give a generalized twisting formula of…

We compute the second moment of the Dedekind zeta function of a quadratic field times an arbitrary Dirichlet polynomial of length $T^{1/11-\epsilon}$.

We generalize a result of Matom\"aki, Radziwi{\l}{\l}, and Tao, by proving an averaged version of a conjecture of Chowla and a conjecture of Elliott regarding correlations of the Liouville function, or more general bounded multiplicative…

Twistec T-adic exponential sums are studied. As an application, the behavior of the L-function under diagonal base chang is explicitely given.

In this note, we demonstrate the convergence of the Demailly approximation of a general (weakly) upper semi-continuous weight.

An exact upper bound on the Winsorised-tilted mean of a symmetric random variable in terms of its second moment is given. Such results are used in work on nonuniform Berry--Esseen-type bounds for general nonlinear statistics.

We study the almost sure convergence of bilateral ergodic averages for not necessarily integrable functions and relate it to the ones of the forward and backward averages, hence complementing results of Wo\'s and the second named author. In…

We introduce the unified double zeta function of Mordell--Tornheim type and compute its values at non-positive integer points. We then discuss a possible generalization of the Kaneko--Zagier conjecture for all integer points.

We give a new and very concise proof of the existence of a holomorphic continuation for a large class of twisted multivariable zeta functions. To do this, we use a simple method of "decalage" that avoids using an integral representation of…

Previously the authors proved subconvexity of Shintani's zeta function enumerating class numbers of binary cubic forms. Here we return to prove subconvexity of the Maass form twisted version.

The generalization of new mock theta functions of Andrews and Bringmann et al are given. Further we have given the expansion of these bilateral generalized new mock theta functions as 2 phi 1 series by Slaters transformation. After that we…

We prove asymptotic formulas for mean square values of the Euler double zeta-function $\zeta_2(s_0,s)$, with respect to $\Im s$. Those formulas enable us to propose a double analogue of the Lindel{\"o}f hypothesis.

Some properties of integral averages of functions on intervals and their asymptotic behavior are investigated. The results are aimed at applications to entire and subharmonic functions.

We evaluate friable averages of arithmetic functions whose Dirichlet series is analytically close to some negative power of the Riemann zeta function. We obtain asymptotic expansions resembling those provided by the Selberg-Delange method…

In this note we derive asymptotic formulas for power mean of the Hurwitz zeta function over large intervals.

Explicit bounds on the tails of the zeta function $\zeta$ are needed for applications, notably for integrals involving $\zeta$ on vertical lines or other paths going to infinity. Here we bound weighted $L^2$ norms of tails of $\zeta$. Two…

In this paper, we investigate the ``shuffle-type'' formula for special values of desingularized multiple zeta functions at integer points. It is proved by giving an iterated integral/differential expression for the desingularized multiple…

Let $\mathfrak{q}>2$ be a prime number, $\chi$ a primitive Dirichlet character modulo $\mathfrak{q}$ and $f$ a primitive holomorphic cusp form or a Hecke-Maass cusp form of level $\mathfrak{q}$ and trivial nebentypus. We prove the subconvex…

We define the adelic hypergeometric function of special Gaussian type by means of a tower of hypergeometric curves. This function takes values in an adelic completed group ring and interpolates all the hypergeometric functions of the same…

We study analytic function interpolating the multiple generalized Euler numbers attached to $\chi$ at negative integers.