Zobrazeno 1 - 10 of 102 pro vyhledávání: '"Christophe Vignat"'
1
On a result of Koecher concerning Markov–Apéry-type formulas for the Riemann zeta function
Autor: Karl Dilcher, Christophe Vignat
Publikováno v: International Journal of Number Theory. 19:709-731
Koecher in 1980 derived a method for obtaining identities for the Riemann zeta function at odd positive integers, including a classical result for [Formula: see text] due to Markov and rediscovered by Apéry. In this paper, we extend Koecher’s meth
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::a0c093e17ce3cfeddd9b2c880beeef83
https://doi.org/10.1142/s1793042123500355
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3
Compatibility of the method of brackets with classical integration rules
Autor: Zachary Bradshaw, Ivan Gonzalez, Lin Jiu, Victor Hugo Moll, Christophe Vignat
Publikováno v: Open Mathematics. 21
The method of brackets is a symbolic approach to the computation of integrals over R n {{\mathbb{R}}}^{n} based on a deep result by Ramanujan. Its usefulness to obtain new and difficult integrals has been demonstrated many times in the last few years
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::1873939012f4016a3ad1783eb8f39547
https://doi.org/10.1515/math-2022-0581
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4
Structural properties of multiple zeta values
Autor: Tanay Wakhare, Christophe Vignat
Publikováno v: International Journal of Number Theory
International Journal of Number Theory, World Scientific Publishing, 2021, 17 (08), pp.1873-1897. ⟨10.1142/S1793042121500676⟩
We study some classical identities for multiple zeta values and show that they still hold for zeta functions built on the zeros of an arbitrary function. We introduce the complementary zeta function of a system, which naturally occurs when lifting id
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2e8268752a738d905bcc7eb5803f5306
https://doi.org/10.1142/s1793042121500676
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5
Taylor coefficients of the Jacobi θ3(q) function
Autor: Christophe Vignat, Tanay Wakhare
Publikováno v: Journal of Number Theory
Journal of Number Theory, Elsevier, 2020, 216, pp.280-306. ⟨10.1016/j.jnt.2020.03.002⟩
We extend some results recently obtained by Dan Romik [14] about the Taylor coefficients of the theta function θ 3 ( e − π ) to the case θ 3 ( q ) of a real valued variable 0 q 1 . These results are obtained by carefully studying the properties
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a8473dfb5de01f2417509ad02d282ce6
https://doi.org/10.1016/j.jnt.2020.03.002
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6
An Operational Calculus Generalization of Ramanujan's Master Theorem
Autor: Zachary P. Bradshaw, Christophe Vignat
We give a formal extension of Ramanujan's master theorem using operational methods. The resulting identity transforms the computation of a product of integrals on the half-line to the computation of a Laplace transform. Since the identity is purely f
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7
Identities for Bernoulli polynomials related to multiple Tornheim zeta functions
Autor: Christophe Vignat, Armin Straub, Karl Dilcher
Publikováno v: Journal of Mathematical Analysis and Applications
Journal of Mathematical Analysis and Applications, Elsevier, 2019, 476 (2), pp.569-584. ⟨10.1016/j.jmaa.2019.03.071⟩
We show that each member of a doubly infinite sequence of highly nonlinear expressions of Bernoulli polynomials, which can be seen as linear combinations of certain higher-order convolutions, is a multiple of a specific product of linear factors. The
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fd18b92aab16d74140ef6271b643253d
https://doi.org/10.1016/j.jmaa.2019.03.071
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8
A triple integral analog of a multiple zeta value
Autor: Victor H. Moll, Christophe Vignat, Armin Straub, Tewodros Amdeberhan
Publikováno v: International Journal of Number Theory
International Journal of Number Theory, World Scientific Publishing, 2021, 17 (02), pp.223-237. ⟨10.1142/S1793042120400102⟩
We establish the triple integral evaluation \[ \int_{1}^{\infty} \int_{0}^{1} \int_{0}^{1} \frac{dz \, dy \, dx}{x(x+y)(x+y+z)} = \frac{5}{24} \zeta(3), \] as well as the equivalent polylogarithmic double sum \[ \sum_{k=1}^{\infty} \sum_{j=k}^{\infty
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6bd7975f226d82720e40dbc26f94dbb2
http://arxiv.org/abs/2004.06232
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9
Analytic continuation for multiple zeta values using symbolic representations
Autor: Christophe Vignat, Tanay Wakhare, Lin Jiu
Publikováno v: International Journal of Number Theory
International Journal of Number Theory, World Scientific Publishing, 2020, 16 (03), pp.579-602. ⟨10.1142/S1793042120500293⟩
We introduce a symbolic representation of $r$-fold harmonic sums at negative indices. This representation allows us to recover and extend some recent results by Duchamp et al., such as recurrence relations and generating functions for these sums. Thi
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::470e32b81f085c07011324eae657c30e
https://hal.archives-ouvertes.fr/hal-02518758
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10
Nonconventional limits of random sequences related to partitions of integers
Autor: Christophe Vignat, Jordan Stoyanov
Publikováno v: Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society, American Mathematical Society, 2020, 148 (4), pp.1791-1804. ⟨10.1090/proc/14638⟩
International audience
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::58b81ca2c8f01b29ea897fadde1be88c
https://hal.archives-ouvertes.fr/hal-02500435
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