کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4665016 | 1633782 | 2017 | 16 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Zeta-polynomials for modular form periods
ترجمه فارسی عنوان
زتا چند جملهای برای دورههای فرم مدولار
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
چکیده انگلیسی
Answering problems of Manin, we use the critical L-values of even weight kâ¥4 newforms fâSk(Î0(N)) to define zeta-polynomials Zf(s) which satisfy the functional equation Zf(s)=±Zf(1âs), and which obey the Riemann Hypothesis: if Zf(Ï)=0, then Re(Ï)=1/2. The zeros of the Zf(s) on the critical line in t-aspect are distributed in a manner which is somewhat analogous to those of classical zeta-functions. These polynomials are assembled using (signed) Stirling numbers and “weighted moments” of critical L-values. In analogy with Ehrhart polynomials which keep track of integer points in polytopes, the Zf(s) encode arithmetic information. Assuming the Bloch-Kato Tamagawa Number Conjecture, they encode the arithmetic of a combinatorial arithmetic-geometric object which we call the “Bloch-Kato complex” for f. Loosely speaking, these are graded sums of weighted moments of orders of Å afareviÄ-Tate groups associated to the Tate twists of the modular motives.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 306, 14 January 2017, Pages 328-343
Journal: Advances in Mathematics - Volume 306, 14 January 2017, Pages 328-343
نویسندگان
Ken Ono, Larry Rolen, Florian Sprung,