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Relevant bibliographies by topics / Lerch's theorem

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Journal articles

Academic literature on the topic 'Lerch's theorem'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 February 2022

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Journal articles on the topic "Lerch's theorem"

1

Dolník, Matej, and Tomáš Kisela. "Lerch’s theorem on nabla time scales." Mathematica Slovaca 69, no. 5 (2019): 1127–36. http://dx.doi.org/10.1515/ms-2017-0295.

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Abstract The paper discusses uniqueness of Laplace transform considered on nabla time scales. As the main result, a nabla time scales analogue of Lerch’s theorem ensuring uniqueness of Laplace image is proved for so-called simply periodic time scales. Moreover, several presented counterexamples demonstrate that the uniqueness of Laplace image does not occur on general time scales when the nabla approach is employed. Other special properties of Laplace transform on nabla time scales, such as potential disconnectedness of domain of convergence, are addressed as well.

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2

WANG, LI-YUAN, and HAI-LIANG WU. "APPLICATIONS OF LERCH’S THEOREM TO PERMUTATIONS OF QUADRATIC RESIDUES." Bulletin of the Australian Mathematical Society 100, no. 3 (2019): 362–71. http://dx.doi.org/10.1017/s000497271900073x.

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Let $n$ be a positive integer and $a$ an integer prime to $n$. Multiplication by $a$ induces a permutation over $\mathbb{Z}/n\mathbb{Z}=\{\overline{0},\overline{1},\ldots ,\overline{n-1}\}$. Lerch’s theorem gives the sign of this permutation. We explore some applications of Lerch’s result to permutation problems involving quadratic residues modulo $p$ and confirm some conjectures posed by Sun [‘Quadratic residues and related permutations and identities’, Preprint, 2018, arXiv:1809.07766]. We also study permutations involving arbitrary $k$th power residues modulo $p$ and primitive roots modulo a power of $p$.

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3

Barnes, K. J. "Avoiding the theorem of Lerche and Shore." Physics Letters B 468, no. 1-2 (1999): 81–85. http://dx.doi.org/10.1016/s0370-2693(99)00865-5.

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4

Tzermias, Pavlos. "A note on a paper by Brenner." International Journal of Mathematics and Mathematical Sciences 31, no. 11 (2002): 701–2. http://dx.doi.org/10.1155/s0161171202202197.

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5

Laurinčikas, Antanas, and Renata Macaitienė˙. "Joint universality of the Riemann zeta-function and Lerch zeta-functions." Nonlinear Analysis: Modelling and Control 18, no. 3 (2013): 314–26. http://dx.doi.org/10.15388/na.18.3.14012.

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In the paper, we prove a joint universality theorem for the Riemann zeta-function and a collection of Lerch zeta-functions with parameters algebraically independent over the field of rational numbers.

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6

Laurinčikas, Antanas, and Kohji Matsumoto. "The joint universality and the functional independence for Lerch zeta-functions." Nagoya Mathematical Journal 157 (2000): 211–27. http://dx.doi.org/10.1017/s002776300000725x.

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The joint universality theorem for Lerch zeta-functions L(λl, αl, s) (1 ≤ l ≤ n) is proved, in the case when λls are rational numbers and αls are transcendental numbers. The case n = 1 was known before ([12]); the rationality of λls is used to establish the theorem for the “joint” case n ≥ 2. As a corollary, the joint functional independence for those functions is shown.

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7

Kutbi, M. A., and A. A. Attiya. "Differential Subordination Results for Certain Integrodifferential Operator and Its Applications." Abstract and Applied Analysis 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/638234.

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We introduce an integrodifferential operatorJs,b(f) which plays an important role in theGeometric Function Theory. Some theorems in differential subordination forJs,b(f) are used. Applications inAnalytic Number Theoryare also obtained which give new results for Hurwitz-Lerch Zeta function and Polylogarithmic function.

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8

Wang, Xiao-Yuan, Lei Shi, and Zhi-Ren Wang. "Certain Integral Operator Related to the Hurwitz–Lerch Zeta Function." Journal of Complex Analysis 2018 (April 8, 2018): 1–7. http://dx.doi.org/10.1155/2018/5915864.

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The aim of the present paper is to investigate several third-order differential subordinations, differential superordination properties, and sandwich-type theorems of an integral operator Ws,bf(z) involving the Hurwitz–Lerch Zeta function. We make some applications of the operator Ws,bf(z) for meromorphic functions.

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9

Laurinčikas, A., and K. Matsumoto. "Joint value-distribution theorems on Lerch zeta-functions. II." Lithuanian Mathematical Journal 46, no. 3 (2006): 271–86. http://dx.doi.org/10.1007/s10986-006-0027-x.

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10

Laurincikas, A., and Kohji Matsumoto. "Joint value-distribution theorems for the Lerch zeta-functions." Lithuanian Mathematical Journal 38, no. 3 (1998): 238–49. http://dx.doi.org/10.1007/bf02465899.

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