Monatshefte für Mathematik

, Volume 173, Issue 4, pp 471–493 | Cite as

Identities for Anderson generating functions for Drinfeld modules

Article

Abstract

Anderson generating functions are generating series for division values of points on Drinfeld modules, and they serve as important tools for capturing periods, quasi-periods, and logarithms. They have been fundamental in recent work on special values of positive characteristic \(L\)-series and in transcendence and algebraic independence problems. In the present paper we investigate techniques for expressing Anderson generating functions in terms of the defining polynomial of the Drinfeld module and determine new formulas for periods and quasi-periods.

Keywords

Drinfeld modules Anderson generating functions shadowed partitions periods quasi-periods Drinfeld logarithms 

Mathematics Subject Classification (1991)

Primary 11G09 Secondary 11B37 12H10 33E50 

Notes

Acknowledgments

We thank the referee for carefully reading the paper and for several helpful suggestions.

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Copyright information

© Springer-Verlag Wien 2013

Authors and Affiliations

  1. 1.Science ProgramTexas A&M University in QatarDohaQatar
  2. 2.Department of Mathematics, Faculty of ScienceCairo UniversityGizaEgypt
  3. 3.Department of MathematicsTexas A&M UniversityCollege StationUSA

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