Two problems related to the non-vanishing of $L (1, \chi )$

Paolo Codecà; Roberto Dvornicich; Umberto Zannier

Displaying similar documents to “Two problems related to the non-vanishing of $L (1, χ)$ ”

On the power-series expansion of a rational function

D. V. Lee (1992)

Acta Arithmetica

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Introduction. The problem of determining the formula for $P_{S} (n)$ , the number of partitions of an integer into elements of a finite set S, that is, the number of solutions in non-negative integers, $h_{s ₁}, . . ., h_{s_{k}}$ , of the equation hs₁ s₁ + ... + hsk sk = n, was solved in the nineteenth century (see Sylvester [4] and Glaisher [3] for detailed accounts). The solution is the coefficient of $x ⁿ i n$ [(1-xs₁)... (1-xsk)]-1, expressions for which they derived. Wright [5] indicated a simpler method by which to find part...

Indirect approximation theorems in $L^{p}$ -metrics $(1 < p < \infty)$

R. Taberski (1979)

Banach Center Publications

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Nonconvolution transforms with oscillating kernels that map $Ḃ_{1}^{0, 1}$ into itself

G. Sampson (1993)

Studia Mathematica

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We consider operators of the form $(Ω f) (y) = ʃ_{- \infty}^{\infty} Ω (y, u) f (u) d u$ with Ω(y,u) = K(y,u)h(y-u), where K is a Calderón-Zygmund kernel and $h \in L^{\infty}$ (see (0.1) and (0.2)). We give necessary and sufficient conditions for such operators to map the Besov space $Ḃ_{1}^{0, 1}$ (= B) into itself. In particular, all operators with $h (y) = e^{{i | y |}^{a}}$ , a > 0, a ≠ 1, map B into itself.

Several $q$ -series identities from the Euler expansions of ${(a; q)}_{\infty}$ and $\frac{1}{{(a; q)}_{\infty}}$

Zhizheng Zhang, Yang, Jizhen (2009)

Archivum Mathematicum

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In this paper, we first give several operator identities which extend the results of Chen and Liu, then make use of them to two $q$ -series identities obtained by the Euler expansions of ${(a; q)}_{\infty}$ and $\frac{1}{{(a; q)}_{\infty}}$ . Several $q$ -series identities are obtained involving a $q$ -series identity in Ramanujan’s Lost Notebook.

The number of solutions of a system of equations in a finite field

Charles Wells (1967)

Acta Arithmetica

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Linear independence of values of a certain generalisation of the exponential function – a new proof of a theorem of Carlson

Rolf Wallisser (2005)

Journal de Théorie des Nombres de Bordeaux

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Let $Q$ be a nonconstant polynomial with integer coefficients and without zeros at the non–negative integers. Essentially with the method of Hermite, a new proof is given on linear independence of values at rational points of the function $\begin{matrix} G (x) = \sum_{n = 0}^{\infty} \frac{x^{n}}{Q (1) Q (2) \dots Q (n)} . \end{matrix}$

On a conjecture of Norton

D. Burgess (1975)

Acta Arithmetica

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On some singular integral operatorsclose to the Hilbert transform

T. Godoy, L. Saal, M. Urciuolo (1997)

Colloquium Mathematicae

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Let m: ℝ → ℝ be a function of bounded variation. We prove the $L^{p} (ℝ)$ -boundedness, 1 < p < ∞, of the one-dimensional integral operator defined by $T_{m} f (x) = p . v . \int k (x - y) m (x + y) f (y) d y$ where $k (x) = \sum_{j \in ℤ} 2^{j} φ_{j} (2^{j} x)$ for a family of functions ${φ_{j}}_{j \in ℤ}$ satisfying conditions (1.1)-(1.3) given below.

Displaying similar documents to “Two problems related to the non-vanishing of L ( 1 , χ ) ”

Displaying similar documents to “Two problems related to the non-vanishing of $L (1, χ)$ ”