Twists and resonance of $L$-functions, I

Jerzy Kaczorowski; Alberto Perelli

Displaying similar documents to “Twists and resonance of $L$ -functions, I”

Uniqueness and differential polynomials of meromorphic functions sharing a nonzero polynomial

Pulak Sahoo (2016)

Mathematica Bohemica

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Let $k$ be a nonnegative integer or infinity. For $a \in ℂ \cup {\infty}$ we denote by $E_{k} (a; f)$ the set of all $a$ -points of $f$ where an $a$ -point of multiplicity $m$ is counted $m$ times if $m \leq k$ and $k + 1$ times if $m > k$ . If $E_{k} (a; f) = E_{k} (a; g)$ then we say that $f$ and $g$ share the value $a$ with weight $k$ . Using this idea of sharing values we study the uniqueness of meromorphic functions whose certain nonlinear differential polynomials share a nonzero polynomial with finite weight. The results of the paper improve and generalize the related results due to...

On the meromorphic solutions of a certain type of nonlinear difference-differential equation

Sujoy Majumder, Lata Mahato (2023)

Mathematica Bohemica

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The main objective of this paper is to give the specific forms of the meromorphic solutions of the nonlinear difference-differential equation $f^{n} (z) + P_{d} (z, f) = p_{1} (z) e^{α_{1} (z)} + p_{2} (z) e^{α_{2} (z)},$ where $P_{d} (z, f)$ is a difference-differential polynomial in $f (z)$ of degree $d \leq n - 1$ with small functions of $f (z)$ as its coefficients, $p_{1}$ , $p_{2}$ are nonzero rational functions and $α_{1}$ , $α_{2}$ are non-constant polynomials. More precisely, we find out the conditions for ensuring the existence of meromorphic solutions of the above equation.

On operators from $ℓ_{s}$ to $ℓ_{p} \otimes ̂ ℓ_{q}$ or to $ℓ_{p} \hat{\otimes ̂} ℓ_{q}$

Christian Samuel (2010)

Colloquium Mathematicae

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We show that every operator from $ℓ_{s}$ to $ℓ_{p} \otimes ̂ ℓ_{q}$ is compact when 1 ≤ p,q < s and that every operator from $ℓ_{s}$ to $ℓ_{p} \hat{\otimes ̂} ℓ_{q}$ is compact when 1/p + 1/q > 1 + 1/s.

On the proximate order of $f^{(s)} (z) * g^{(s)} (z)$ and ${[f (z) * g (z)]}^{(s)}$

M. K. Sen (1971)

Annales Polonici Mathematici

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Addendum to “On the $p^{λ}$ problem”

Stephan Baier (2005)

Acta Arithmetica

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A characterization of the disc $D^{n}$

Th. Friedrich (1974)

Colloquium Mathematicae

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A pure smoothness condition for Radó’s theorem for $α$ -analytic functions

Abtin Daghighi, Frank Wikström (2016)

Czechoslovak Mathematical Journal

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Let $Ω \subset ℂ^{n}$ be a bounded, simply connected $ℂ$ -convex domain. Let $α \in ℤ_{+}^{n}$ and let $f$ be a function on $Ω$ which is separately $C^{2 α_{j} - 1}$ -smooth with respect to $z_{j}$ (by which we mean jointly $C^{2 α_{j} - 1}$ -smooth with respect to $Re z_{j}$ , $Im z_{j}$ ). If $f$ is $α$ -analytic on $Ω ∖ f^{- 1} (0)$ , then $f$ is $α$ -analytic on $Ω$ . The result is well-known for the case $α_{i} = 1$ , $1 \leq i \leq n$ , even when $f$ a priori is only known to be continuous.