Frontiers of Mathematics in China >

2012 , Vol. 7 >Issue 5: 883 - 894

DOI: https://doi.org/10.1007/s11464-012-0238-x

RESEARCH ARTICLE

Estimates of generalized Chebyshev function on GLm

  • Yan QU 1 ,
  • Shuai ZHAI , 2
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  • 1. Institute of Mathematics, Chinese Academy of Sciences, Beijing 100190, China
  • 2. School of Mathematics, Shandong University, Jinan 250100, China

Received date: 16 Feb 2012

Accepted date: 07 Aug 2012

Published date: 01 Oct 2012

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

In this paper, we study the generalized Chebyshev function related to automorphic L-functions of GLm(ℚ), and estimate its asymptotic behavior with respect to the parameters of the original automorphic objects.

Key words： Automorphic L-function; Chebyshev function; explicit formula; conductor

Cite this article

Yan QU , Shuai ZHAI . Estimates of generalized Chebyshev function on GLm[J]. Frontiers of Mathematics in China, 2012 , 7(5) : 883 -894 . DOI: 10.1007/s11464-012-0238-x

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
1. Gallagher P X. A large sieve density estimate near σ= 1. Invent Math, 1970, 11: 329-339

DOI

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

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

8
8. Qu Y. The prime number theorem for automorphic L-functions for GLm. J Number Theory, 2007, 122: 84-99

DOI

9
9. Tenenbaum G. Introduction to Analytic and Probabilistic Number Theory. Cambridge: Cambridge University Press, 1995

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

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