A formula for the central value of certain Hecke L-functions
Let N ≡ 1 mod 4 be the negative of a prime, K = ℚ(√N) and OK its ring of integers. Let D be a prime ideal in OK of prime norm congruent to 3 mod 4. Under these assumptions, there exists Hecke characters ψD of K with conductor (D) and infinite type (1, 0). Their L-series L (ψD, s) are associated to a...
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2005
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0022314X_v113_n2_p339_Pacetti |
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paperaa:paper_0022314X_v113_n2_p339_Pacetti2023-06-12T16:44:40Z A formula for the central value of certain Hecke L-functions J. Number Theory 2005;113(2):339-379 Pacetti, A. Hecke L-functions Let N ≡ 1 mod 4 be the negative of a prime, K = ℚ(√N) and OK its ring of integers. Let D be a prime ideal in OK of prime norm congruent to 3 mod 4. Under these assumptions, there exists Hecke characters ψD of K with conductor (D) and infinite type (1, 0). Their L-series L (ψD, s) are associated to a CM elliptic curve A(N, D) defined over the Hilbert class field of K. We will prove a Waldspurger-type formula for L(ψD, s) of the form L(ψD, 1) = Ω∑[A],Ir (D, [A], I) m[A],I ([D]) where the sum is over class ideal representatives I of a maximal order in the quaternion algebra ramified at N and infinity and [A] are class group representatives of K. An application of this formula for the case N = -7 will allow us to prove the non-vanishing of a family of L-series of level 7 D over K. © 2005 Elsevier Inc. All rights reserved. Fil:Pacetti, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2005 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0022314X_v113_n2_p339_Pacetti |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| language |
Inglés |
| orig_language_str_mv |
eng |
| topic |
Hecke L-functions |
| spellingShingle |
Hecke L-functions Pacetti, A. A formula for the central value of certain Hecke L-functions |
| topic_facet |
Hecke L-functions |
| description |
Let N ≡ 1 mod 4 be the negative of a prime, K = ℚ(√N) and OK its ring of integers. Let D be a prime ideal in OK of prime norm congruent to 3 mod 4. Under these assumptions, there exists Hecke characters ψD of K with conductor (D) and infinite type (1, 0). Their L-series L (ψD, s) are associated to a CM elliptic curve A(N, D) defined over the Hilbert class field of K. We will prove a Waldspurger-type formula for L(ψD, s) of the form L(ψD, 1) = Ω∑[A],Ir (D, [A], I) m[A],I ([D]) where the sum is over class ideal representatives I of a maximal order in the quaternion algebra ramified at N and infinity and [A] are class group representatives of K. An application of this formula for the case N = -7 will allow us to prove the non-vanishing of a family of L-series of level 7 D over K. © 2005 Elsevier Inc. All rights reserved. |
| format |
Artículo Artículo publishedVersion |
| author |
Pacetti, A. |
| author_facet |
Pacetti, A. |
| author_sort |
Pacetti, A. |
| title |
A formula for the central value of certain Hecke L-functions |
| title_short |
A formula for the central value of certain Hecke L-functions |
| title_full |
A formula for the central value of certain Hecke L-functions |
| title_fullStr |
A formula for the central value of certain Hecke L-functions |
| title_full_unstemmed |
A formula for the central value of certain Hecke L-functions |
| title_sort |
formula for the central value of certain hecke l-functions |
| publishDate |
2005 |
| url |
http://hdl.handle.net/20.500.12110/paper_0022314X_v113_n2_p339_Pacetti |
| work_keys_str_mv |
AT pacettia aformulaforthecentralvalueofcertainheckelfunctions AT pacettia formulaforthecentralvalueofcertainheckelfunctions |
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1769810380418187264 |