Doi–Naganuma lifting

In mathematics, the Doi–Naganuma lifting is a map from elliptic modular forms to Hilbert modular forms of a real quadratic field, introduced by Doi & Naganuma (1969) and Naganuma (1973). It was a precursor of the base change lifting.

It is named for Japanese mathematicians Kōji Doi (土井公二） and Hidehisa Naganuma (長沼英久).

See also

• Saito–Kurokawa lift, a similar lift to Siegel modular forms

References

• Doi, Koji; Naganuma, Hidehisa (1967), "On the algebraic curves uniformized by arithmetical automorphic functions", Annals of Mathematics, Second Series, 86: 449–460, doi:10.2307/1970610, ISSN 0003-486X, JSTOR 1970610, MR 0219537
• Doi, Koji; Naganuma, Hidehisa (1969), "On the functional equation of certain Dirichlet series", Inventiones Mathematicae, 9 (1): 1–14, doi:10.1007/BF01389886, ISSN 0020-9910, MR 0253990
• Naganuma, Hidehisa (1973), "On the coincidence of two Dirichlet series associated with cusp forms of Hecke's "Neben"-type and Hilbert modular forms over a real quadratic field", Journal of the Mathematical Society of Japan, 25 (4): 547–555, doi:10.2969/jmsj/02540547, ISSN 0025-5645, MR 0332661