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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
Статьи
Zeta integrals on arithmetic surfaces
T. Oliver Heilbronn Institute for Mathematical Research, University of Bristol, UK
Аннотация:
Given a (smooth, projective, geometrically connected) curve over a number field, one expects its Hasse–Weil $L$-function, a priori defined only on a right half-plane, to admit meromorphic continuation to $\mathbb C$ and satisfy a simple functional equation. Aside from exceptional circumstances, these analytic properties remain largely conjectural. One may formulate these conjectures in terms of zeta functions of two-dimensional arithmetic schemes, on which one has non-locally compact “analytic” adelic structures admitting a form of “lifted” harmonic analysis first defined by Fesenko for elliptic curves. In this paper we generalize his global results to certain curves of arbitrary genus by invoking a renormalizing factor which may be interpreted as the zeta function of a relative projective line. We are lead to a new interpretation of the “gamma factor” (defined in terms of the Hodge structures at archimedean places) and an (two-dimensional) adelic interpretation of the “mean-periodicity correspondence”, which is comparable to the conjectural automorphicity of Hasse–Weil $L$-functions.
Ключевые слова:
scheme of finite type, zeta function, local field, Hasse–Weil $L$-function, complete discrete valuation field, adeles.
Полный текст:
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Англоязычная версия:
St. Petersburg Mathematical Journal, 2016, 27:6, 1003–1028
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Тип публикации:
Статья Поступила в редакцию: 27.02.2015
Язык публикации: английский
Образец цитирования:
T. Oliver, “Zeta integrals on arithmetic surfaces”, Алгебра и анализ, 27:6 (2015), 199–233; St. Petersburg Math. J., 27:6 (2016), 1003–1028
Цитирование в формате AMSBIB
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http://mi.mathnet.ru/aa1473 http://mi.mathnet.ru/rus/aa/v27/i6/p199
Citing articles on Google Scholar:
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Related articles on Google Scholar:
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English articles
Эта публикация цитируется в следующих статьяx:
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T. Oliver, “Automorphicity and mean-periodicity”, J. Math. Soc. Jpn., 69:1 (2017), 25–51
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