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<?xml version='1.0' encoding='iso-8859-1'?>
<!DOCTYPE cedram SYSTEM 'cedram.dtd'>
<!-- Translated from latex by tralics 2.13.7, date: 2010/10/26-->
<cedram>
<article><production>
<fichier_tex>bo</fichier_tex>
<fichier_bib>bo</fichier_bib>
<date_prod>2010-10-26</date_prod></production>
<date_reception>2004-06-14</date_reception>
<date_acceptation>2004-12-09</date_acceptation>
<auteur>
<prenom>Donald</prenom>
<middlename>E.</middlename>
<nom><hi rend='it'>Knuth</hi></nom>
<adresse><TeX/> Users Group P.O. Box 869 Santa Barbara, CA 93102-0869 USA</adresse>
<mel>d.e.knuth@somewhere.on.the.net</mel>
</auteur>
<titre xml:lang='fr'>Coefficients Fourier pour fonctions <formula type='inline'><math xmlns='http://www.w3.org/1998/Math/MathML'><msup><mi>L</mi> <mi>∞</mi> </msup></math></formula> simples</titre>
<TeXtitre xml:lang='fr'>Coefficients Fourier pour fonctions <texmath textype='inline' type='inline'>L^\infty </texmath> simples</TeXtitre>
<titre xml:lang='en'>Fourier coefficients for simple <formula type='inline'><math xmlns='http://www.w3.org/1998/Math/MathML'><msup><mi>L</mi> <mi>∞</mi> </msup></math></formula> functions</titre>
<TeXtitre xml:lang='en'>Fourier coefficients for simple <texmath textype='inline' type='inline'>L^\infty </texmath> functions</TeXtitre>
<langue>en</langue>
<resume xml:lang='en'>This is an abstract with a beautiful inline formula <formula type='inline'><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><msub><mi>λ</mi> <mi>n</mi> </msub><mrow><mo>(</mo><mi>π</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mi>N</mi> <mn>2</mn></mfrac><mi>n</mi><mo form='prefix'>log</mo><mi>n</mi><mo>+</mo><msub><mi>C</mi> <mn>1</mn> </msub><mrow><mo>(</mo><mi>π</mi><mo>)</mo></mrow><mi>n</mi><mo>+</mo><mi>O</mi><mrow><mo>(</mo><msqrt><mi>n</mi></msqrt><mo form='prefix'>log</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></formula>, where <formula type='inline'><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><msub><mi>C</mi> <mn>1</mn> </msub><mrow><mo>(</mo><mi>π</mi><mo>)</mo></mrow></mrow></math></formula> is a real-valued constant.
</resume>
<TEXresume xml:lang='en'>This is an abstract with a beautiful inline formula <texmath textype='inline' type='inline'>\lambda _n(\pi ) = \frac{N}{2} n \log n + C_1(\pi ) n +
O(\sqrt{n}\log {n})</texmath>, where <texmath textype='inline' type='inline'>C_1(\pi )</texmath> is a real-valued constant.
</TEXresume>
<resume xml:lang='fr'>Mon rsum avec ma formule
<formula type='inline'><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><msub><mi>λ</mi> <mi>n</mi> </msub><mrow><mo>(</mo><mi>π</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mi>N</mi> <mn>2</mn></mfrac><mi>n</mi><mo form='prefix'>log</mo><mi>n</mi><mo>+</mo><msub><mi>C</mi> <mn>1</mn> </msub><mrow><mo>(</mo><mi>π</mi><mo>)</mo></mrow><mi>n</mi><mo>+</mo><mi>O</mi><mrow><mo>(</mo><msqrt><mi>n</mi></msqrt><mo form='prefix'>log</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></formula>, o <formula type='inline'><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><msub><mi>C</mi> <mn>1</mn> </msub><mrow><mo>(</mo><mi>π</mi><mo>)</mo></mrow></mrow></math></formula> est une constante relle.
</resume>
<TEXresume xml:lang='fr'>Mon rsum avec ma formule
<texmath textype='inline' type='inline'>\lambda _n(\pi ) = \frac{N}{2} n \log n + C_1(\pi ) n +
O(\sqrt{n}\log {n})</texmath>, o <texmath textype='inline' type='inline'>C_1(\pi )</texmath> est une constante relle.
</TEXresume>
<motcle xml:lang='fr'>fonctions <formula type='inline'><math xmlns='http://www.w3.org/1998/Math/MathML'><msup><mi>L</mi> <mi>∞</mi> </msup></math></formula> simples, fonction lambda</motcle>
<motcle xml:lang='en'>simple <formula type='inline'><math xmlns='http://www.w3.org/1998/Math/MathML'><msup><mi>L</mi> <mi>∞</mi> </msup></math></formula> functions, lambda function</motcle>
<msc>11M26, 11M36, 11S40</msc>
</article>
<p/><biblio>
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<bjournal>Messenger of Math.</bjournal>
<bvolume>33</bvolume>
<byear>1903</byear>
<bpages>59–61</bpages>
</citation>
<citation from='year' key='Bom00' id='bid2' userid='cite:Bo99' type='article'>
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<title>Remarks on Weil's quadratic functional in the theory of prime numbersI</title>
<bjournal>Rend. Mat. Acc. Lincei, Ser.IX</bjournal>
<bvolume>11</bvolume>
<byear>2000</byear>
<bpages>183–233</bpages>
</citation>
<citation from='year' key='BPY01' id='bid1' userid='cite:BPY01' type='article'>
<bauteurs><nom>Biane</nom><prenom>P.</prenom><initiale>P.</initiale><particule/><junior/><nom>Pitman</nom><prenom>J.</prenom><initiale>J.</initiale><particule/><junior/><nom>Yor</nom><prenom>M.</prenom><initiale>M.</initiale><particule/><junior/></bauteurs>
<title>Probability laws related to the Jacobi $\theta$ and Riemann $\zeta$ functions, and Brownian excursions</title>
<bjournal>Bull. Amer. Math. Soc.</bjournal>
<bvolume>38</bvolume>
<byear>2001</byear>
<bpages>435–465</bpages>
</citation></biblio></cedram>
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