Academic Journal
Exceptional zero formulae for anticyclotomic p-adic L-functions of elliptic curves in the ramified case
| العنوان: | Exceptional zero formulae for anticyclotomic p-adic L-functions of elliptic curves in the ramified case |
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| المؤلفون: | Longo Matteo, Pati, Maria Rosaria |
| المساهمون: | Longo, Matteo, Pati, MARIA ROSARIA, Maria, Rosaria |
| بيانات النشر: | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| سنة النشر: | 2018 |
| المجموعة: | Padua Research Archive (IRIS - Università degli Studi di Padova) |
| مصطلحات موضوعية: | Elliptic curve, Iwasawa theory, p-adic L-function |
| الوصف: | Iwasawa theory of modular forms over anticyclotomic Zp-extensions of imaginary quadratic fields K has been studied by several authors, starting from the works of Bertolini–Darmon and Iovita–Spiess, under the crucial assumption that the prime p is unramified in K. We start in this article the systematic study of anticyclotomic p-adic L-functions when p is ramified in K. In particular, when f is a weight 2 modular form attached to an elliptic curve E/Q having multiplicative reduction at p, and p is ramified in K, we show an analogue of the exceptional zeroes phenomenon investigated by Bertolini–Darmon in the setting when p is inert in K. More precisely, we consider situations in which the p-adic L-function Lp(E/K) of E over the anticyclotomic Zp-extension of K does not vanish identically but, by sign reasons, has a zero at certain characters χ of the Hilbert class field of K. In this case we show that the value at χ of the first derivative of Lp(E/K) is equal to the formal group logarithm of the specialization at p of a global point on the elliptic curve (actually, this global point is a twisted sum of Heegner points). This generalizes similar results of Bertolini–Darmon, available when p is inert in K and χ is the trivial character. |
| نوع الوثيقة: | article in journal/newspaper |
| وصف الملف: | STAMPA |
| اللغة: | English |
| Relation: | info:eu-repo/semantics/altIdentifier/wos/WOS:000434105800010; volume:190; firstpage:187; lastpage:211; numberofpages:25; journal:JOURNAL OF NUMBER THEORY; http://hdl.handle.net/11577/3281242; info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-85043990639 |
| DOI: | 10.1016/j.jnt.2018.02.010 |
| الاتاحة: | http://hdl.handle.net/11577/3281242 https://doi.org/10.1016/j.jnt.2018.02.010 |
| Rights: | info:eu-repo/semantics/openAccess |
| رقم الانضمام: | edsbas.4FF14456 |
| قاعدة البيانات: | BASE |
| DOI: | 10.1016/j.jnt.2018.02.010 |
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