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  • 2005-2009
  • 1975-1979  (6)
  • 1978  (6)
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  • 2005-2009
  • 1975-1979  (6)
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  • 1
    Electronic Resource
    Electronic Resource
    Fourier coefficients of cusp forms (1978)
    Springer
    Inventiones mathematicae 45 (1978), S. 1-18 
    Details
    ISSN: 1432-1297
    Keywords: Cusp forms ; Fourier coefficients ; Modular group
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let ψ1,ψ2,ψ3,... be an orthonormal basis of the space of cusp forms of weight zero for the full modular group. Let be the Fourier series expansion. The following theorem is proved: Let σ∈(1/4, 1/2); letf be a holomorphic function on the strip |Res|≦σ, satisfyingf(−s)=f(s) and $$f(s) = \mathcal{O}(|\tfrac{1}{4} - s^2 |^{ - 2} |cos \pi s|^{ - 1} )$$ on this strip; letm andn be non-zero integers, then $$\sum\limits_{j = 1}^\infty {f(s_j )\bar \gamma _{jm} \gamma _{jn} } $$ converges and is equal to $$\begin{gathered} - (2\pi i)^{ - 1} \int\limits_{\operatorname{Re} s = 0} {f(s)c_{00} ( - s)c_{0|m|} (s)c_{0|n|} (s)ds} \hfill \\ + (2\pi i)^{ - 1} (4\pi |m|)^{ - 1} \int\limits_{\operatorname{Re} s = 0} {f(s)c_{mn} (s)2sds} \hfill \\ - \delta _{mn} (2\pi i)^{ - 1} (4\pi |m|)^{ - 1} \int\limits_{\operatorname{Re} s = 0} {f(s)\sin \pi s2sds.} \hfill \\ \end{gathered} $$ The functionsc 00(s) andc 0|m|(s) are coefficients occurring in the Fourier series expansion of the Eisenstein series; the functionc mn(s) is a coefficient in the Fourier series expansion of a Poincaré series. The theorem is applied to obtain some asymptotic results concerning the Fourier coefficients γjn. Under additional conditions on the functionf the formula in the theorem is modified in such a way that the Fourier coefficients of holomorphic cusp forms appear.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01406220
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  • 2
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    Purification of Vitellogenin mRNA and Serum Albumin mRNA from Avian Liver by Preparative Gel Electrophoresis (1978)
    Wiley
    Details
    Publication Date: 1978-08-01
    Print ISSN: 0014-2956
    Electronic ISSN: 1432-1033
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Published by Wiley on behalf of Federation of European Biochemical Societies.
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  • 3
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    Notes on Fissidens. I and II (1978)
    In:  Mededelingen van het Botanisch Museum en Herbarium van de Rijksuniversiteit te Utrecht (2352-5754) vol.469 (1978) nr.1 p.387
    Details
    Publication Date: 2015-05-08
    Description: In Note I it is shown that the delimitation of the sections Bryoidium, Pachylomidium, Aloma and Semilimbidium subsect. Bryolimbidium is very vague. Consequently they are united. The resulting section contains the type species of the genus Fissidens and the correct name for it is, therefore, Fissidens. In Note II F. bambergeri Schimp. ex Milde, F. firmus Linb. ex Roth, F. herzogii Ruthe in Herzog, F. canariensis Bryhn and F. bilewskyi Pot. Varde are reduced to synonymy under F. minutulus Sull. F. minutulus is described, figured and characterized. Besides, it is compared with F. ovatifolius Ruthe. F. pusillus (Wils.) Milde, F. minutulus Sull. and F. viridulus (Swartz) Wahl, are compared and found to be three distinct species. F. subimmarginatus Phil, is reduced to synonymy under F. exiguus Sull.
    Repository Name: National Museum of Natural History, Netherlands
    Type: Article / Letter to the editor
    Format: application/pdf
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  • 4
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    A new species of Fissidens from Tanzania (1978)
    In:  Mededelingen van het Botanisch Museum en Herbarium van de Rijksuniversiteit te Utrecht (2352-5754) vol.498 (1978) nr.1 p.249
    Details
    Publication Date: 2015-05-08
    Description: Fissidens splendens Brugg.-Nann. – nov. spec. – Type: Pócs 6289 Z (herbarium Bizot: holotype; U). – Fig. 1-7. Species lamina vera semi-aperta vel raro, aperta et limbo folii tumido e cellulis parenchymaticis composito instructa faciliter distinguenda. A F. nitente s.l. limbo cellulis prosenohymaticis carente differt.
    Repository Name: National Museum of Natural History, Netherlands
    Type: Article / Letter to the editor
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  • 5
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    Notes on Fissidens. I and II (1978)
    In:  Mededelingen van het Botanisch Museum en Herbarium van de Rijksuniversiteit te Utrecht vol. 469 no. 1, pp. 387-402
    Details
    Publication Date: 2024-01-12
    Description: In Note I it is shown that the delimitation of the sections Bryoidium, Pachylomidium, Aloma and Semilimbidium subsect. Bryolimbidium is very vague. Consequently they are united. The resulting section contains the type species of the genus Fissidens and the correct name for it is, therefore, Fissidens.\nIn Note II F. bambergeri Schimp. ex Milde, F. firmus Linb. ex Roth, F. herzogii Ruthe in Herzog, F. canariensis Bryhn and F. bilewskyi Pot. Varde are reduced to synonymy under F. minutulus Sull. F. minutulus is described, figured and characterized. Besides, it is compared with F. ovatifolius Ruthe.\nF. pusillus (Wils.) Milde, F. minutulus Sull. and F. viridulus (Swartz) Wahl, are compared and found to be three distinct species. F. subimmarginatus Phil, is reduced to synonymy under F. exiguus Sull.
    Repository Name: National Museum of Natural History, Netherlands
    Type: info:eu-repo/semantics/article
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  • 6
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    A new species of Fissidens from Tanzania (1978)
    In:  Mededelingen van het Botanisch Museum en Herbarium van de Rijksuniversiteit te Utrecht vol. 498 no. 1, pp. 249-251
    Details
    Publication Date: 2024-01-12
    Description: Fissidens splendens Brugg.-Nann. \xe2\x80\x93 nov. spec. \xe2\x80\x93 Type: P\xc3\xb3cs 6289 Z (herbarium Bizot: holotype; U). \xe2\x80\x93 Fig. 1-7.\nSpecies lamina vera semi-aperta vel raro, aperta et limbo folii tumido e cellulis parenchymaticis composito instructa faciliter distinguenda. A F. nitente s.l. limbo cellulis prosenohymaticis carente differt.
    Repository Name: National Museum of Natural History, Netherlands
    Type: info:eu-repo/semantics/article
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