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Nature, 1953
Funzioni Abeliane Modulari Lezioni raccolte dal Dott. Mario Rosati. Per Fabio Conforto. Vol. 1: Preliminari e parte gruppale; geometria simplettica. Pp. 454. (Roma: Edizioni Universitarie Docet, 1951.) 3900 lire.
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Funzioni Abeliane Modulari Lezioni raccolte dal Dott. Mario Rosati. Per Fabio Conforto. Vol. 1: Preliminari e parte gruppale; geometria simplettica. Pp. 454. (Roma: Edizioni Universitarie Docet, 1951.) 3900 lire.
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The modular group and modular functions
1976In the foregoing chapter we encountered unimodular transformations $$ {{c\tau + d}} $$ where a, b, c, d are integers with ad — bc = 1. This chapter studies such transformations in greater detail and also studies functions which, Iike J(τ), are invariant under unimodular transformations.
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Rendiconti del Circolo Matematico di Palermo, 2004
The paper is related to the classical theorem of Lyapunov which says that an \(R^n\)-valued atomless \(\sigma\)-additive measure on a \(\sigma\)-algebra has a convex range. \textit{G. Knowles} [SIAM J. Control 13, 294--303 (1974; Zbl 0302.49005)] generalized this theorem for non-injective measures with values in locally convex spaces. \textit{P.
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The paper is related to the classical theorem of Lyapunov which says that an \(R^n\)-valued atomless \(\sigma\)-additive measure on a \(\sigma\)-algebra has a convex range. \textit{G. Knowles} [SIAM J. Control 13, 294--303 (1974; Zbl 0302.49005)] generalized this theorem for non-injective measures with values in locally convex spaces. \textit{P.
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2000
It is the purpose of the authors to use \(n\)th order theta functions to construct some modular forms of weight 0 on the groups \(\Gamma_0 (p)\), \(p\) a prime (Theorem 1), \(\Gamma^0(p^2)\), \(p\) a prime (Theorem 2) and \(\theta(n)=\Gamma_0 \setminus\operatorname{cap} \Gamma_\vartheta\), \(n\in\mathbb{Z}^+\) (Theorem 3).
KIRMACI, Uğur Selamet +1 more
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It is the purpose of the authors to use \(n\)th order theta functions to construct some modular forms of weight 0 on the groups \(\Gamma_0 (p)\), \(p\) a prime (Theorem 1), \(\Gamma^0(p^2)\), \(p\) a prime (Theorem 2) and \(\theta(n)=\Gamma_0 \setminus\operatorname{cap} \Gamma_\vartheta\), \(n\in\mathbb{Z}^+\) (Theorem 3).
KIRMACI, Uğur Selamet +1 more
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Classical Modular Symbols, Modular Forms, L-functions
2021We introduce the classical modular symbols, which are modular symbols with coefficients polynomials of bounded degree. We explain their close connection with modular forms, and with their L-functions.
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1987
By SL2 we mean the group of 2 x 2 matrices with determinant 1. We write SL2 (R) for those elements of SL2 having coefficients in a ring R. In practice, the ring R will be Z, Q, R. We call SL2 (Z) the modular group.
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By SL2 we mean the group of 2 x 2 matrices with determinant 1. We write SL2 (R) for those elements of SL2 having coefficients in a ring R. In practice, the ring R will be Z, Q, R. We call SL2 (Z) the modular group.
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Composition and functions of bacterial membrane vesicles
Nature Reviews Microbiology, 2023Masanori Toyofuku +2 more
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