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Generalized maass wave forms
No full textWe initiate the study of generalized Maass wave forms, those Maass wave forms for which the multiplier system is not necessarily unitary. We then prove some basic theorems inherited from the classical theory of modular forms with a generalization of some examples from the classical theory of Maass forms. © 2012 American Mathematical Society.Borel A., 1997, CAMBRIDGE TRACTS MAT, V130; Bruggeman R.W., 1981, LECT NOTES MATH, V865; BRUGGEMAN RW, 1978, INVENT MATH, V45, P1, DOI 10.1007-BF01406220; Bruggeman R.W., 1994, MONOGRAPHS MATH, V88; Bruinier JH, 2009, MATH ANN, V345, P31, DOI 10.1007-s00208-009-0338-4; Bruinier JH, 2008, MATH ANN, V342, P673, DOI 10.1007-s00208-008-0252-1; Bump Daniel, 1997, CAMBRIDGE STUDIES AD, V55, DOI DOI 10.1017-CBO9780511609572; Dong CY, 2000, COMMUN MATH PHYS, V214, P1, DOI 10.1007-s002200000242; Eichler M., 1957, MATH Z, V67, P267, DOI 10.1007-BF01258863; Eichler M., 1965, ACTA ARITH, V11, P169; Iwaniec H., 2002, GRADUATE STUDIES MAT, V53; Knopp M, 2004, ILLINOIS J MATH, V48, P1345; Knopp M, 2010, INT J NUMBER THEORY, V6, P1083, DOI 10.1142-S179304211000340X; Knopp M, 2003, ACTA ARITH, V110, P117, DOI 10.4064-aa110-2-2; Knopp M, 2003, J NUMBER THEORY, V99, P1, DOI 10.1016-S0022-314X(02)00065-3; Knopp M, 2009, INT J NUMBER THEORY, V5, P1049, DOI 10.1142-S1793042109002547; KNOPP MI, 1974, B AM MATH SOC, V80, P607, DOI 10.1090-S0002-9904-1974-13520-2; Lewis J, 2001, ANN MATH, V153, P191, DOI 10.2307-2661374; Maass H., 1983, LECT MODULAR FUNCTIO; Magnus Wilhelm, 1966, GRUND MATH WISS, V52; Mayer H., 1991, B AM MATH SOC, V25, P55; Muhlenbruch T, 2006, J NUMBER THEORY, V118, P208, DOI 10.1016-j.jnt.2005.09.003; Muhlenbruch T., 2003, THESIS UTRECHT U; Raji W, 2009, FUNCT APPROX COMM MA, V41, P105; Raji W, 2009, INT J NUMBER THEORY, V5, P153; Zhu YC, 1996, J AM MATH SOC, V9, P237, DOI 10.1090-S0894-0347-96-00182-811
