×

zbMATH — the first resource for mathematics

Periods of mixed cusp forms. (English) Zbl 0759.11020
We define the periods of mixed cusp forms and establish generalized Eichler-Shimura relations for the periods of mixed cups forms. We also construct modular symbols for mixed cusp forms and express the periods of mixed cusp forms in terms of these modular symbols.

MSC:
11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)
14J25 Special surfaces
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] B. Birch, Elliptic curves overQ: a progress report, AMS Proc. Symp. Pure Math.20 (1971), 396–400
[2] M. Eichler, Eine Verallgemeinerung der Abelschen Integrale, Math. Z.67 (1957), 267–298 · Zbl 0080.06003
[3] B. Hunt and W. Meyer, Mixed automorphic forms and invariants of elliptic surfaces, Math. Ann.271 (1985), 53–80 · Zbl 0552.14008
[4] N. Koblitz, Congruences for periods of modular forms, Duke Math. J.54 (1987), 361–373 · Zbl 0628.10032
[5] K. Kodaira, On compact analytic surfaces II–III, Ann. Math.77 (1963), 563–626;78 (1963), 1–40 · Zbl 0118.15802
[6] M. H. Lee, Mixed cusp forms and holomorphic forms on elliptic varieties, Pac. J. Math.132 (1988), 363–370 · Zbl 0648.14017
[7] Y. Manin, Cyclotomic fields and modular curves, Russian Math. Surveys26 (1971), 7–78 · Zbl 0266.14012
[8] Y. Manin, Parabolic points and zeta functions of modular curves, Math. USSR Izv.6 (1972), 19–64 · Zbl 0248.14010
[9] Y. Manin, Periods of parabolic forms andp-adic Hecke series, Math USSR Sb.21 (1973), 371–393 · Zbl 0293.14008
[10] M. Razar, Values of Dirichlet series at integers in the critical strip, Modular Functions of One Variable VI, Springer (1977), 1–10 · Zbl 0366.10021
[11] G. Shimura, Sur les intégrales attachées aux formes automorphes, J. Math. Soc. Japan11 (1959), 291–311 · Zbl 0090.05503
[12] V. Ŝokurov, The study of the homology of Kuga varieties, Math. USSR Izv.16 (1981), 399–418 · Zbl 0462.14013
[13] V. Ŝokurov, Shimura integrals of cusp forms, Math. USSR Izv.16 (1981), 603–646 · Zbl 0466.14014
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.