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    Blomer, Valentin and Milićević, Djordje 2015. The Second Moment of Twisted Modular L-Functions. Geometric and Functional Analysis, Vol. 25, Issue. 2, p. 453.

    Motohashi, Y. 2015. On sums of Hecke-Maass eigenvalues squared over primes in short intervals. Journal of the London Mathematical Society, Vol. 91, Issue. 2, p. 367.

    Sun, Qingfeng 2015. On effective determination of symmetric-square lifts, level aspect. International Journal of Number Theory, Vol. 11, Issue. 01, p. 51.

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    Blomer, Valentin 2013. Applications of the Kuznetsov formula on GL(3). Inventiones mathematicae, Vol. 194, Issue. 3, p. 673.

    Li, Xiaoqing and Young, Matthew P. 2012. The L2 restriction norm of a GL3 Maass form. Compositio Mathematica, Vol. 148, Issue. 03, p. 675.

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On the Exceptional Zeros of Rankin–Selberg L-Functions

  • Dinakar Ramakrishnan (a1) and Song Wang (a2)
  • DOI:
  • Published online: 01 January 2003

The main objects of study in this article are two classes of Rankin–Selberg L-functions, namely L(s,f×g) and L(s, sym2(g)× sym2(g)), where f,g are newforms, holomorphic or of Maass type, on the upper half plane, and sym2(g) denotes the symmetric square lift of g to GL(3). We prove that in general, i.e., when these L-functions are not divisible by L-functions of quadratic characters (such divisibility happening rarely), they do not admit any LandauSiegel zeros. Such zeros, which are real and close to s=1, are highly mysterious and are not expected to occur. There are corollaries of our result, one of them being a strong lower bound for special value at s=1, which is of interest both geometrically and analytically. One also gets this way a good bound on the norm of sym2(g).

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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