Related papers: Lamprecht-Tate Formula
In this paper, we establish an asymptotic formula for the twisted second moments of Dirichlet $L$-functions with one and two twists when averaged over all primitive Dirichlet characters of modulus $R$, where $R$ is a monic polynomial in…
In this paper, we study certain Kummer characters, which we call the elliptic Soul\'e characters, arising from Galois actions on the pro-$p$ fundamental groups of once-punctured elliptic curves with complex multiplication. In particular, we…
We determine the distribution of discriminants of wildly ramified elementary-abelian extensions of local and global function fields in characteristic $p$. For local and rational function fields, we also give precise formulae for the number…
This is a semi-expository paper on the easier aspects of the Explicit Formula for the Riemann Zeta Function. The topics reviewed here include: Weil's criterion for the Riemann Hypothesis and its probabilistic interpretation, various…
In the present paper, a generalized local Taylor formula with the local fractional derivatives (LFDs) is proposed based on the local fractional calculus (LFC). From the fractal geometry point of view, the theory of local fractional…
In this article we consider a class of non-degenerate elliptic operators obtained by superpositioning the Laplacian and a general nonlocal operator. We study the existence-uniqueness results for Dirichlet boundary value problems, maximum…
Some nonlocal and nonpolynomial scalar field models originated from p-adic string theory are considered. Infinite number of spacetime derivatives is governed by the Riemann zeta function through d'Alembertian $\Box$ in its argument.…
The paper begins with a novel variational formulation of Duffing equation using the extended framework of Hamilton's principle (EHP). This formulation properly accounts for initial conditions, and it recovers all the governing differential…
We can attach a local constant to every finite dimensional continuous complex representation of a local Galois group of a non-archimedean local field $F/\mathbb{Q}_p$ by Deligne and Langlands. Tate \cite{JT1} gives an explicit formula for…
We prove an epsilon-regularity theorem for critical and super-critical systems with a non-local antisymmetric operator on the right-hand side. These systems contain as special cases, Euler-Lagrange equations of conformally invariant…
We consider moments of higher powers of quadratic Dirichlet character sums. In a restricted region, we give their asymptotic behavior by using de la Bret\`{e}che's multivariable Tauberian theorem. We also give the lower bound of the…
We studies the Newton polygon for the L-function of toric exponential sums attached to a family of two variable generalized hyperkloosterman sum,$f_{t}(x,y)=x^{n}+y+\frac{t}{xy}$ with $t$ the parameter. The explicit Newton polygon is…
An unusual formula for the Euler characteristics of even dimensional triangulated manifolds is deduced from the generalized Dehn-Sommerville equations.
A classical result of Littlewood gives a factorisation for the Schur function at a set of variables "twisted" by a primitive $t$-th root of unity, characterised by the core and quotient of the indexing partition. While somewhat neglected,…
When a matrix has a banded inverse there is a remarkable formula that quickly computes that inverse, using only local information in the original matrix. This local inverse formula holds more generally, for matrices with sparsity patterns…
We extend in two directions the notion of perturbations of Carleson type for the Dirichlet problem associated to an elliptic real second-order divergence-form (possibly degenerate, not necessarily symmetric) elliptic operator. First, in…
We prove a new determinantal formula for the characters of irreducible representations of orthosymplectic Lie superalgebras analogous to the formula developed by Moens and Jeugt (J. Algebraic Combin., 2003) for general linear Lie…
We give an apparently new proof of Stirling's original asymptotic formula for the behavior of $\ln z!$ for large $z$. Stirling's original formula is not the formula widely known as "Stirling's formula", which was actually due to De Moivre.…
The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…
We establish an asymptotic formula with a power-saving error term for the twisted mixed moment of Dirichlet $L$-functions and automorphic $L$-functions twisted by all primitive characters modulo $q$, valid for all admissible moduli. As a…