Journal of the Ramanujan Mathematical Society

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On Simultaneous Non-Vanishing Of Twisted L-Fnctions Associated to Newforms on Γ0(N)


Affiliations
1 Department of Mathematics, Indian Institute of science, Bangalore 560 012, India
2 Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad 211 004, India
3 Harish-Chandra Research Institute, HBNI, Allahabad, India
     

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Given two normalized Hecke eigenforms f1, f2 of weight k1 and k2 respectively of squarefree level N, we consider the product of twisted L-functions associated with f1 and f2 by a quadratic charater χ, and show that if this product does not vanish at the center of the critical strip s = 1/2, then it does not vanish for infinitely many such twists. This is a generalisation of the work due to R. Munshi (J. Number Theory, 132, 666-674 [2012]) for the full modular group to the case of any congruence subgroup of squarfree level N.
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  • Shamita Dutta Gupta, The Rankin-Selberg method on congruence subgroups, Illinois J. Math., 44 no. 1, (2000) 95–103.

  • H. Iwaniec and E. Kowalski, Analytic number theory, Amer. Math. Soc. Colloq. Publ., Vol. 53 American Mathematical Society, Providence, RI (2004).

  • N. Koblitz, Introduction to elliptic curves and modular forms, Second Edition, Graduate Texts in Mathematics, Springer, 97 (1993).

  • W. Kohnen, Newforms of half-integral weight, J. Reine Angew. Math., 333 (1982) 32–72.

  • W. Kohnen, Fourier coefficients of modular forms of half-integral weight, Math. Ann., 271 (1985) 237–268.

  • R. Munshi, A note on simultaneous nonvanishing twists, J. Number Theory, 132 (2012) 666–674.

  • G. Shimura, On modular forms of half integral weight, Ann. of Math. (2), 97 (1973) 440–481.


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  • On Simultaneous Non-Vanishing Of Twisted L-Fnctions Associated to Newforms on Γ0(N)

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Authors

Abhash Kumar Jha
Department of Mathematics, Indian Institute of science, Bangalore 560 012, India
Abhishek Juyal
Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad 211 004, India
Manish Kumar Pandey
Harish-Chandra Research Institute, HBNI, Allahabad, India

Abstract


Given two normalized Hecke eigenforms f1, f2 of weight k1 and k2 respectively of squarefree level N, we consider the product of twisted L-functions associated with f1 and f2 by a quadratic charater χ, and show that if this product does not vanish at the center of the critical strip s = 1/2, then it does not vanish for infinitely many such twists. This is a generalisation of the work due to R. Munshi (J. Number Theory, 132, 666-674 [2012]) for the full modular group to the case of any congruence subgroup of squarfree level N.

References