충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제30권2호
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  • Pages.183-200
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  • 2017
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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TWO ZAGIER-LIFTS

  • Kang, Soon-Yi (Department of Mathematics Kangwon National University)
  • 투고 : 2016.11.28
  • 심사 : 2017.02.28
  • 발행 : 2017.05.15
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초록

Zagier lift gives a relation between weakly holomorphic modular functions and weakly holomorphic modular forms of weight 3/2. Duke and Jenkins extended Zagier-lifts for weakly holomorphic modular forms of negative-integral weights and recently Bringmann, Guerzhoy and Kane extended them further to certain harmonic weak Maass forms of negative-integral weights. New Zagier-lifts for harmonic weak Maass forms and their relation with Bringmann-Guerzhoy-Kane's lifts were discussed earlier. In this paper, we give explicit relations between the two different lifts via direct computation.

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과제정보

연구 과제 주관 기관 : National Research Foundation of Korea(NRF)

참고문헌

  1. K. Bringmann, P. Guerzhoy, and B. Kane, Shintani lifts and fractional derivatives for harmonic weak Maass forms, Adv. Math. 255 (2014), 641-671. https://doi.org/10.1016/j.aim.2014.01.015
  2. J. H. Bruinier and J. Funke, On two geometric theta lifts, Duke Math. J. 125 (2004), no. 1, 45-90. https://doi.org/10.1215/S0012-7094-04-12513-8
  3. W. Duke and P. Jenkins, Integral traces of singular values of weak Maass form, Algebra and Number Theory 2 (2008), no. 5, 573-593. https://doi.org/10.2140/ant.2008.2.573
  4. W. Duke, O. Imamoglu, and A. Toth, Cycle integrals of the j-function and mock modular forms, Ann. Math. 173 (2011), no. 2, 947-981. https://doi.org/10.4007/annals.2011.173.2.8
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  7. D. Jeon, S.-Y. Kang, and C. H. Kim, Zagier-lift type arithmetic in harmonic weak Maass forms, J. Number Theory 169 (2016), 227-249. https://doi.org/10.1016/j.jnt.2016.05.012
  8. W. Kohnen, Fourier coefficients of modular forms of half-integral weight, Math. Ann. 271 (1985), 237-268. https://doi.org/10.1007/BF01455989
  9. D. Zagier, Traces of singular moduli, Motives, polylogarithms and Hodge theory, Part I, Irvine, CA, 1998, International Press Lecture Series 3, Part I (Int. Press, Somerville, MA, 2002) 211-244.