Results 41 to 50 of about 7,783 (125)
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
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Tube domains and restrictions of minimal representations
, 2007 In this paper we study the restrictions of the minimal representation in the analytic continuation of the scalar holomorphic discrete series from $Sp(n,\mathbb{R})$ to $GL(n,\mathbb{R})$, and from SU(n,n) to $GL(n,\mathbb{C})$ respectively.
Seppanen, Henrik
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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
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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$\lbrace a(
Wing Hong Leung
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, 1989 I. Fourier transforms on L1 (-?,?).- 1. Basic properties and examples.- 2. The L1 -algebra.- 3. Differentiability properties.- 4. Localization, Mellin transforms.- 5. Fourier series and Poisson's summation formula.- 6.
K. Chandrasekharan
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Bilinear sums with GL(2)$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
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Some Applications of Laplace Transforms in Analytic Number Theory [PDF]
, 2014 In this overview paper, presented at the meeting DANS14, Novi Sad, July3-7, 2014, we give some applications of Laplace transforms to analytic number theory.
Ivić, Aleksandar
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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
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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.
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On the Mellin transforms of powers of Hardy's function
, 2010 Various properties of the Mellin transform function $$ {\cal M}_k(s) := \int_1^\infty Z^k(x)x^{-s}dx $$ are investigated, where $$ Z(t) := \zeta(1/2+it){\bigl(\chi(1/2+it)\bigr)}^{-1/2}, \quad \zeta(s) = \chi(s)\zeta(1-s) $$ is Hardy's function and ...
Ivić, Aleksandar
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