Value-Distribution of L-Functions
L-functions are important objects in modern number theory. They are gen- ating functions formed out of local data associated with either an arithmetic object or with an automorphic form. They can be attached to smooth p- jective varieties de?ned over number ?elds, to irreducible (complex orp-adic) r...
שמור ב:
| מחבר ראשי: | |
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| פורמט: | Livre numérique |
| שפה: | Anglais |
| יצא לאור: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| מהדורה: | 1st ed. 2007. |
| סדרה: | Lecture Notes in Mathematics
1877 |
| נושאים: | |
| גישה מקוונת: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| הערה: |
L'impression du document génère 319 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Value-distribution of L-functions, Jörn Steuding, 2007, Berlin, Springer, 1 vol. (XIII-317 p.), Lecture notes in mathematics, 978-3-540-26526-9 • Value-Distribution of L-Functions, Texte imprimé, 9783540812319 • Value-distribution of L-functions, Jörn Steuding, 2007, Berlin, Springer, 1 vol. (XIII-317 p.), Lecture notes in mathematics, 978-3-540-26526-9 |
| סיכום: | L-functions are important objects in modern number theory. They are gen- ating functions formed out of local data associated with either an arithmetic object or with an automorphic form. They can be attached to smooth p- jective varieties de?ned over number ?elds, to irreducible (complex orp-adic) representations of the Galois group of a number ?eld, to a cusp form or to an irreducible cuspidal automorphic representation. All theL-functions have in common that they can be described by an Euler product, i. e. , a product takenoverprimenumbers. Inviewoftheuniqueprimefactorizationofintegers L-functions also have a Dirichlet series representation. The famous Riemann zeta-function ? ?1 1 1 ?(s)= = 1? s s n p n=1 pprime may be regarded as the prototype. L-functions encode in their val- distribution information on the underlying arithmetic or algebraic structure that is often not obtainable by elementary or algebraic methods. For instance, Dirichlet s class number formula gives information on the deviation from unique prime factorization in the ring of integers of quadratic number ?elds by the values of certain DirichletL-functionsL(s,?) ats=1. In parti- lar, the distribution of zeros ofL-functions is of special interest with respect to many problems in multiplicative number theory. A ?rst example is the Riemann hypothesis on the non-vanishing of the Riemann zeta-function in the right half of the critical strip and its impact on the distribution of prime numbers. Another example areL-functionsL(s,E) attached to elliptic curves E de?ned over Q |
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| תאור פריט: | L'impression du document génère 319 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ביבליוגרפיה: | Bibliogr. Index |
| ISBN: | 9783540448228 |
| ISSN: | 1617-9692 |
| גישה: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |