کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4591188 | 1335015 | 2010 | 25 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Modified zeta functions as kernels of integral operators
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
The modified zeta functions ∑n∈Kn−s, where K⊂N, converge absolutely for . These generalise the Riemann zeta function which is known to have a meromorphic continuation to all of C with a single pole at s=1. Our main result is a characterisation of the modified zeta functions that have pole-like behaviour at this point. This behaviour is defined by considering the modified zeta functions as kernels of certain integral operators on the spaces L2(I) for symmetric and bounded intervals I⊂R. We also consider the special case when the set K⊂N is assumed to have arithmetic structure. In particular, we look at local Lp integrability properties of the modified zeta functions on the abscissa for p∈[1,∞].
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 259, Issue 2, 15 July 2010, Pages 359-383
Journal: Journal of Functional Analysis - Volume 259, Issue 2, 15 July 2010, Pages 359-383