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Estimates of generalized Chebyshev function on GLm |
Yan QU1, Shuai ZHAI2( ) |
| 1. Institute of Mathematics, Chinese Academy of Sciences, Beijing 100190, China; 2. School of Mathematics, Shandong University, Jinan 250100, China |
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Abstract In this paper, we study the generalized Chebyshev function related to automorphic L-functions of GLm(??), and estimate its asymptotic behavior with respect to the parameters of the original automorphic objects.
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| Keywords
Automorphic L-function
Chebyshev function
explicit formula
conductor
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Corresponding Author(s):
ZHAI Shuai,Email:zhaishuai@mail.sdu.edu.cn
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Issue Date: 01 October 2012
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| 1 |
1. Gallagher P X. A large sieve density estimate near σ= 1. Invent Math , 1970, 11: 329-339 doi: 10.1007/BF01403187
|
| 2 |
2. Gallagher P X. Some consequences of the Riemann hypothesis. Acta Arith , 1980, 37: 339-343
|
| 3 |
3. Ingham A E. The Distribution of Prime Numbers. Cambridge: Cambridge University Press, 1932
|
| 4 |
4. Iwaniec H, Kowalski E. Analytic Number Theory. Providence: Amer Math Soc, 2004
|
| 5 |
5. Liu J, Ye Y. Superpositions of distinct L-functions. Forum Math , 2002, 14: 419-455 doi: 10.1515/form.2002.020
|
| 6 |
6. Liu J, Ye Y. Perron’s formula and the prime number theorem for automorphic L-functions. Pure Appl Math Q , 2007, 3: 481-497
|
| 7 |
7. Luo W, Rudnick Z, Sarnak P. On Selberg’s eigenvalue conjecture. Geom Funct Anal , 1995, 5: 387-401 doi: 10.1007/BF01895672
|
| 8 |
8. Qu Y. The prime number theorem for automorphic L-functions for GLm. J Number Theory , 2007, 122: 84-99 doi: 10.1016/j.jnt.2006.03.007
|
| 9 |
9. Tenenbaum G. Introduction to Analytic and Probabilistic Number Theory. Cambridge: Cambridge University Press, 1995
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| 10 |
10. Wu J, Ye Y. Hypothesis H and the prime number theorem for automorphic representations. Funct Approx Comment Math , 2007, 37(2): 461-471 doi: 10.7169/facm/1229619665
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