118 research outputs found
EICHLER COHOMOLOGY OF GENERALIZED MODULAR FORMS OF REAL WEIGHTS
No full textIn this paper, we prove the Eichler cohomology theorem of weakly parabolic generalized modular forms of real weights on subgroups of finite index in the full modular group. We explicitly establish the isomorphism for large weights by constructing the map from the space of cusp forms to the cohomology group. © 2012 American Mathematical Society.Bol G., 1949, ABH MATH SEM HAMBURG, V16, P1; Eichler M., 1965, ACTA ARITH, V11, P169; HUSSEINI SY, 1971, ILLINOIS J MATH, V15, P565; Knopp M, 2010, INT J NUMBER THEORY, V6, P1083, DOI 10.1142-S179304211000340X; Knopp M, 2003, J NUMBER THEORY, V99, P1, DOI 10.1016-S0022-314X(02)00065-3; Knopp M, 2009, INT J NUMBER THEORY, V5, P845, DOI 10.1142-S1793042109002419; 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; Niebur D., 1968, THESIS MADISON; NIEBUR D, 1974, T AM MATH SOC, V191, P373, DOI 10.2307-1997003; Petersson H., 1950, SB HEIDELBERGER A MN, p[417, 806]; Raji W, 2011, INT J NUMBER THEORY, V7, P1103, DOI 10.1142-S1793042111004514; Raji W, 2009, FUNCT APPROX COMM MA, V41, P105; Raji W, 2009, INT J NUMBER THEORY, V5, P15310
Fourier coefficients of generalized modular forms of negative weight
No full textThe Fourier coefficients of classical modular forms of negative weights have been determined for the case for which F(τ) belongs to a subgroup of the full modular group [9]. In this paper, we determine the Fourier coefficients of generalized modular forms of negative weights using the circle method. © World Scientific Publishing Company.DIAMOND F, 2005, FIRST COURSE MODULAR; Eichler M., 1965, ACTA ARITH, V11, P169; 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; Lehner J., 1959, MICH MATH J, V6, P173; LEHNER J, 1957, MICH MATH J, V4, P265; Rademacher H, 1938, ANN MATH, V39, P433, DOI 10.2307-1968796; RAJI W, EICHLER COHOMO UNPUB; Zuckerman HS, 1939, T AM MATH SOC, V45, P298, DOI 10.2307-199011956
q-expansions of vector-valued modular forms of negative weight
No full textIn this paper, we determine the q-expansions of vector-valued modular forms (Knopp and Mason in Ill. J. Math. 48:1345-1366, 2004; Acta Arith. 110(2): 117-124, 2003) of large negative weight on the full modular group where we allow poles in the upper half plane and at infinity. © 2011 Springer Science+Business Media, LLC.Eichler M., 1965, ACTA ARITH, V11, P169; Gimenez J., 2007, THESIS TEMPLE U; Knopp M, 2004, ILLINOIS J MATH, V48, P1345; Knopp M, 2003, ACTA ARITH, V110, P117, DOI 10.4064-aa110-2-2; Rademacher H, 1938, ANN MATH, V39, P433, DOI 10.2307-1968796; Raji W, 2009, INT J NUMBER THEORY, V5, P153; Zuckerman HS, 1940, AM J MATH, V62, P127, DOI 10.2307-23714430
THE COVID PANDEMIC: RESPONSE OF THE RAJI REVITALIZATION PROGRAMMES
No full textRaji is a little known tribal community that resides in twelve geographically scattered hamlets in the state of Uttarakhand, India. According to 2011 Census, their total population is 732. Their language belongs to Tibeto-Burman family. Since, last twenty years or so the author has been working with this group and trying to document, preserve and revitalize their language and culture. Language revitalization requires tackling problems on many fronts and its different approaches depend upon the unique local conditions of the speech community. The author is trying to develop a new revitalization model called \u27South Asian Model of Language Revitalization\u27. This paper discusses the Response of the Raji Revitalization Program towards the present pandemic and sheds light upon the effect of the Covid-19 pandemic on the Raji community and the status of their language
EICHLER COHOMOLOGY THEOREM FOR GENERALIZED MODULAR FORMS
No full text We show starting with relations between Fourier coefficients of weakly parabolic generalized modular forms of negative weight that we can construct automorphic integrals for large integer weights. We finally prove an Eichler isomorphism theorem for weakly parabolic generalized modular forms using the classical approach as in [3]. </jats:p
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Raji Orthography Development
No full textRaji is a little known tribal community whose descendants are the prehistoric Kiratas. They live in dense forests far away from the surrounding Kumauni villages of Pithoragarh district, in the state of Uttarakhand, India. In 2001 census their population was reported to be 680 in all the nine villages. Sir George Grierson, in his book ‘Linguistic Survey of India’ had named this language as ‘janggali which has only spoken form.' Following the framework established by Wurm and the stages of threatenedness discussed in Fishman’s GIDS, Raji can be assessed as ‘potentially endangered andat stage 6 (language) which means the language is at risk.’ While chalking out a revitalization programme for this oral language the author realized the need of orthography development for this language. It is an established fact that Orthography gives stability to a language and not only conserves it but also helps in its standardization. So after preparing a small grammar book, with the help of collected phonologicaland grammatical material of Raji the next important task before the researcher was to develop an orthography system. The present paper focuses on the early stages of orthography development for this previously undocumented indigenous language
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
That wonderful composite called author: Authorship in East Asian literatures from the beginnings to the seventeenth century
No full textEichler cohomology for generalized modular forms
No full textBy using Stokes's theorem, we prove an Eichler cohomology theorem for generalized modular forms with some restrictions on the relevant multiplier systems. © 2009 World Scientific Publishing Company.Bol G., 1949, ABH MATH SEM HAMBURG, V16, P1; Eichler M., 1957, MATH Z, V67, P267, DOI 10.1007-BF01258863; Eichler M., 1965, ACTA ARITH, V11, P169; Ford L. R., 1929, AUTOMORPHIC FUNCTION; Gunning R., 1961, T AM MATH SOC, V100, P44, DOI 10.2307-1993353; HUSSEINI SY, 1971, ILLINOIS J MATH, V15, P565; Knopp M, 2003, ACTA ARITH, V110, P117, DOI 10.4064-aa110-2-2; KNOPP M, INT J NUMBER THEORY; Knopp M, 2003, J NUMBER THEORY, V99, P1, DOI 10.1016-S0022-314X(02)00065-3; Knopp M., 1962, T AM MATH SOC, V103, P168, DOI 10.2307-1993746; KNOPP M, 1965, DUKE MATH J, V32, P452; KNOPP M, 1974, B AM MATH SOC, V50, P607; Knopp M. I., 1993, MODULAR FUNCTIONS AN; KRA I, 1969, ANN MATH, V90, P576, DOI 10.2307-1970749; LEHNER J, 1971, P SCI RES COUNC ATL, P49; LEHNER J, 1969, J RES NBS B MATH SCI, VB 73, P153, DOI 10.6028-jres.073B.016; PETERSSON H, 1937, MATH ANN, V115, P175; RAJI W, EICHLER COHOMO UNPUB; Raji W, 2009, INT J NUMBER THEORY, V5, P153; Shimura G., 1959, J MATH SOC JAPAN, V11, P29155
The compilator as the narrator: Awareness of authorship, authorial presence and author figurations in Japanese imperial anthologies, with a special focus on the Kokin wakashū
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