کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9496519 | 1335840 | 2005 | 26 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
An arithmetic formula for certain coefficients of the Euler product of Hecke polynomials
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: An arithmetic formula for certain coefficients of the Euler product of Hecke polynomials An arithmetic formula for certain coefficients of the Euler product of Hecke polynomials](/preview/png/9496519.png)
چکیده انگلیسی
In 1997 the author found a criterion for the Riemann hypothesis for the Riemann zeta function, involving the nonnegativity of certain coefficients associated with the Riemann zeta function. In 1999 Bombieri and Lagarias obtained an arithmetic formula for these coefficients using the “explicit formula” of prime number theory. In this paper, the author obtains an arithmetic formula for corresponding coefficients associated with the Euler product of Hecke polynomials, which is essentially a product of L-functions attached to weight 2 cusp forms (both newforms and oldforms) over Hecke congruence subgroups Î0(N). The nonnegativity of these coefficients gives a criterion for the Riemann hypothesis for all these L-functions at once.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 113, Issue 1, July 2005, Pages 175-200
Journal: Journal of Number Theory - Volume 113, Issue 1, July 2005, Pages 175-200
نویسندگان
Xian-Jin Li,