Fischler, Stéphane ; Sprang, Johannes ; Zudilin, Wadim
Alternative Links zum Volltext:DOIVerlag
| Dokumentenart: | Artikel |
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| Titel eines Journals oder einer Zeitschrift: | Compositio Mathematica |
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| Verlag: | CAMBRIDGE UNIV PRESS |
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| Ort der Veröffentlichung: | CAMBRIDGE |
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| Band: | 155 |
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| Nummer des Zeitschriftenheftes oder des Kapitels: | 5 |
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| Seitenbereich: | S. 938-952 |
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| Datum: | 2019 |
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| Institutionen: | Mathematik > Prof. Dr. Guido Kings |
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| Identifikationsnummer: | | Wert | Typ |
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| 10.1112/S0010437X1900722X | DOI |
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| Stichwörter / Keywords: | NUMBERS ZETA(5); irrationality; zeta values; hypergeometric series |
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| Dewey-Dezimal-Klassifikation: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
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| Status: | Veröffentlicht |
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| Begutachtet: | Ja, diese Version wurde begutachtet |
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| An der Universität Regensburg entstanden: | Ja |
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| Dokumenten-ID: | 48701 |
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Zusammenfassung
Building upon ideas of the second and third authors, we prove that at least 2((1-epsilon)(log s)/(log log s)) values of the Riemann zeta function at odd integers between 3 and s are irrational, where epsilon is any positive real number and s is large enough in terms of epsilon. This lower bound is asymptotically larger than any power of log s; it improves on the bound (1 - epsilon)(log s) / (1 + ...
Zusammenfassung
Building upon ideas of the second and third authors, we prove that at least 2((1-epsilon)(log s)/(log log s)) values of the Riemann zeta function at odd integers between 3 and s are irrational, where epsilon is any positive real number and s is large enough in terms of epsilon. This lower bound is asymptotically larger than any power of log s; it improves on the bound (1 - epsilon)(log s) / (1 + log 2) that follows from the Ball-Rivoal theorem. The proof is based on construction of several linear forms in odd zeta values with related coefficients.
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