## On the first moment of the symmetric-square $L$-function

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**141**(2013), 369-375 Request permission

## Abstract:

We improve the error term in the asymptotic formula for the twisted first moment of the symmetric-square $L$-function on the critical line.## References

- Tom M. Apostol,
*Introduction to analytic number theory*, Undergraduate Texts in Mathematics, Springer-Verlag, New York-Heidelberg, 1976. MR**0434929** - Valentin Blomer,
*On the central value of symmetric square $L$-functions*, Math. Z.**260**(2008), no.ย 4, 755โ777. MR**2443329**, DOI 10.1007/s00209-008-0299-4 - Satadal Ganguly, Jeffrey Hoffstein, and Jyoti Sengupta,
*Determining modular forms on $\textrm {SL}_2(\Bbb Z)$ by central values of convolution $L$-functions*, Math. Ann.**345**(2009), no.ย 4, 843โ857. MR**2545869**, DOI 10.1007/s00208-009-0380-2 - I. S. Gradshteyn and I. M. Ryzhik,
*Table of integrals, series, and products*, 7th ed., Elsevier/Academic Press, Amsterdam, 2007. Translated from the Russian; Translation edited and with a preface by Alan Jeffrey and Daniel Zwillinger; With one CD-ROM (Windows, Macintosh and UNIX). MR**2360010** - Henryk Iwaniec and Emmanuel Kowalski,
*Analytic number theory*, American Mathematical Society Colloquium Publications, vol. 53, American Mathematical Society, Providence, RI, 2004. MR**2061214**, DOI 10.1090/coll/053 - H. Iwaniec and P. Michel,
*The second moment of the symmetric square $L$-functions*, Ann. Acad. Sci. Fenn. Math.**26**(2001), no.ย 2, 465โ482. MR**1833252** - Rizwanur Khan,
*The first moment of the symmetric-square $L$-function*, J. Number Theory**124**(2007), no.ย 2, 259โ266. MR**2321361**, DOI 10.1016/j.jnt.2006.09.010 - Winfried Kohnen and Jyoti Sengupta,
*Nonvanishing of symmetric square $L$-functions of cusp forms inside the critical strip*, Proc. Amer. Math. Soc.**128**(2000), no.ย 6, 1641โ1646. MR**1676328**, DOI 10.1090/S0002-9939-99-05419-2 - Yuk-Kam Lau,
*Non-vanishing of symmetric square $L$-functions*, Proc. Amer. Math. Soc.**130**(2002), no.ย 11, 3133โ3139. MR**1912989**, DOI 10.1090/S0002-9939-02-06712-6 - Yuk-Kam Lau and Kai-Man Tsang,
*A mean square formula for central values of twisted automorphic $L$-functions*, Acta Arith.**118**(2005), no.ย 3, 231โ262. MR**2168765**, DOI 10.4064/aa118-3-2 - Xian-Jin Li,
*On the poles of Rankin-Selberg convolutions of modular forms*, Trans. Amer. Math. Soc.**348**(1996), no.ย 3, 1213โ1234. MR**1333393**, DOI 10.1090/S0002-9947-96-01540-1 - Goro Shimura,
*On the holomorphy of certain Dirichlet series*, Proc. London Math. Soc. (3)**31**(1975), no.ย 1, 79โ98. MR**382176**, DOI 10.1112/plms/s3-31.1.79

## Additional Information

**Qingfeng Sun**- Affiliation: School of Mathematics and Statistics, Shandong University at Weihai, Weihai 264209, Peopleโs Republic of China
- Email: qfsun@mail.sdu.edu.cn
- Received by editor(s): November 7, 2010
- Published electronically: November 6, 2012
- Additional Notes: The author was supported by the National Natural Science Foundation of China (Grant No. 11101239).
- Communicated by: Ken Ono
- © Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**141**(2013), 369-375 - MSC (2000): Primary 11F67
- DOI: https://doi.org/10.1090/S0002-9939-2012-11564-3
- MathSciNet review: 2996941