Constant terms of Eisenstein series over a totally real field
| Autor: | Tomomi Ozawa |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Rational number
Pure mathematics Algebra and Number Theory Mathematics - Number Theory Mathematics::Number Theory 11F41 (Primary) 11F30 (Secondary) 010102 general mathematics Field (mathematics) Special values Constant term 01 natural sciences Equivalence class (music) symbols.namesake 0103 physical sciences Eisenstein series FOS: Mathematics symbols Congruence (manifolds) Number Theory (math.NT) 010307 mathematical physics 0101 mathematics Real field Mathematics |
| Zdroj: | International Journal of Number Theory. 13:309-324 |
| ISSN: | 1793-7310 1793-0421 |
| DOI: | 10.1142/s1793042117500208 |
| Popis: | In this paper, we compute constant terms of Eisenstein series defined over a totally real field, at various cusps. In his paper published in 2003, M. Ohta computed the constant terms of Eisenstein series of weight two over the field of rational numbers, at all equivalence classes of cusps. As for Eisenstein series defined over a totally real field, S. Dasgupta, H. Darmon and R. Pollack calculated the constant terms at particular (not all) equivalence classes of cusps in 2011. We compute constant terms of Eisenstein series defined over a general totally real field at all equivalence classes of cusps, and describe them explicitly in terms of Hecke $L$-functions. This investigation is motivated by M. Ohta's work on congruence modules related to Eisenstein series defined over the field of rational numbers. 22 pages |
| Databáze: | OpenAIRE |
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