Results 21 to 30 of about 4,568 (108)

Moments of symmetric square L$L$‐functions on GL(3)${\rm GL}(3)$

Proceedings of the London Mathematical Society, Volume 130, Issue 3, March 2025.
Abstract We give an asymptotic formula with power saving error term for the twisted first moment of symmetric square L$L$‐functions on GL(3)${\rm GL}(3)$ in the level aspect. As applications, we obtain nonvanishing results as well as lower bounds of the expected order of magnitude for all even moments, supporting the random matrix model for a unitary ...
Valentin Blomer, Félicien Comtat
wiley   +1 more source

On the Finite Meijer G‐Transformation: Orthogonality, Operational Calculus, and Function Space Analysis

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
In this paper, finite Meijer G‐transformation has been defined. A system of eigenfunctions is verified for the orthogonality condition. Operational calculus properties are shown. The classical concept of finite Meijer G‐transforms is studied in the present text.
Yashonanda Maurya, V. R. Lakshmi Gorty, Shikha Binwal   +2 more
wiley   +1 more source

Solution of Fractional Kinetic Equations Involving New Extended Incomplete Second Appell Hypergeometric Matrix Functions

Journal of Function Spaces, Volume 2025, Issue 1, 2025.
In this paper, we introduce a new extension of the incomplete second Appell hypergeometric matrix functions (EISAHMFs) and extension of the second Appell hypergeometric matrix functions (ESAHMFs) in terms of the extended incomplete Pochhammer matrix symbols and extended Pochhammer matrix symbols, respectively.
Muneera Abdullah Qadha, Sarah Abdullah Qadha, Yusuf Gurefe   +2 more
wiley   +1 more source

Tubings, chord diagrams, and Dyson–Schwinger equations

Journal of the London Mathematical Society, Volume 110, Issue 5, November 2024.
Abstract We give series solutions to single insertion place propagator‐type systems of Dyson–Schwinger equations using binary tubings of rooted trees. These solutions are combinatorially transparent in the sense that each tubing has a straightforward contribution.
Paul‐Hermann Balduf, Amelia Cantwell, Kurusch Ebrahimi‐Fard, Lukas Nabergall, Nicholas Olson‐Harris, Karen Yeats   +5 more
wiley   +1 more source

Reconstruction of an initial function from the solutions of the fractional wave equation on the light cone trace

Mathematical Methods in the Applied Sciences, Volume 47, Issue 12, Page 9469-9475, August 2024.
We reconstruct the initial functions from the trace of the solution of an initial value problem for the wave equation on the light cone. A method to recover the initial function from the solution of the wave equation on the light cone is already known for odd spatial dimensions.
Dabin Park, Sunghwan Moon
wiley   +1 more source

High moments of theta functions and character sums

Mathematika, Volume 70, Issue 2, April 2024.
Abstract Assuming the Generalised Riemann Hypothesis, we prove a sharp upper bound on moments of shifted Dirichlet L‐functions. We use this to obtain conditional upper bounds on high moments of theta functions. Both of these results strengthen theorems of Munsch, who proved almost sharp upper bounds for these quantities.
Barnabás Szabó
wiley   +1 more source

Shifted convolution sums for GL(3)×GL(2)$GL(3)\times GL(2)$ averaged over weighted sets

Mathematika, Volume 70, Issue 2, April 2024.
Abstract Let A(1,m)$A(1,m)$ be the Fourier coefficients of an SL(3,Z)$SL(3,\mathbb {Z})$ Hecke–Maass cusp form F$F$ and λ(m)$\lambda (m)$ be those of an SL(2,Z)$SL(2,\mathbb {Z})$ Hecke holomorphic or Hecke–Maass cusp form g$g$. Let H⊂⟦−X1−ε,X1+ε⟧$\mathcal {H}\subset \llbracket -X^{1-\varepsilon },X^{1+\varepsilon }\rrbracket$ and {a(h)}h∈H⊂C$\lbrace a(
Wing Hong Leung
wiley   +1 more source

Bilinear sums with GL(2)$GL(2)$ coefficients and the exponent of distribution of d3$d_3$

Proceedings of the London Mathematical Society, Volume 128, Issue 3, March 2024.
Abstract We obtain the exponent of distribution 1/2+1/30$1/2+1/30$ for the ternary divisor function d3$d_3$ to square‐free and prime power moduli, improving the previous results of Fouvry–Kowalski–Michel, Heath‐Brown and Friedlander–Iwaniec. The key input is certain estimates on bilinear sums with GL(2)$GL(2)$ coefficients obtained using the delta ...
Prahlad Sharma
wiley   +1 more source

Zeros of dirichlet L‐functions near the critical line

Mathematika, Volume 70, Issue 1, January 2024.
Abstract We prove an upper bound on the density of zeros very close to the critical line of the family of Dirichlet L‐functions of modulus q at height T. To do this, we derive an asymptotic for the twisted second moment of Dirichlet L‐functions uniformly in q and t.
George Dickinson
wiley   +1 more source

Fractional Quadruple Laplace Transform and its Properties

, 2018
In this paper, we introduce definition for fraction al quadruple Laplace transform of order α,0 < fractional differentiable functions. Some main properties and inversion theorem of fractional quadruple Laplace transform are established.
S. Savitha, G. Monisha.
semanticscholar   +1 more source