ترغب بنشر مسار تعليمي؟ اضغط هنا

Higher exponential maps and explicit reciprocity laws I

54   0   0.0 ( 0 )
 نشر من قبل Sarah Livia Zerbes
 تاريخ النشر 2010
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

This paper has been withdrawn, as it is superseded by arXiv:0806.2122 (Bloch-Kato exponential maps for local fields with imperfect residue fields), which is a more recent version of the same paper.

قيم البحث

اقرأ أيضاً

We prove that the central values of additive twists of a cuspidal $L$-function define a quantum modular form in the sense of Zagier, generalizing recent results of Bettin and Drappeau. From this we deduce a reciprocity law for the twisted first momen t of multiplicative twists of cuspidal $L$-functions, similar to reciprocity laws discovered by Conrey for the twisted second moment of Dirichlet $L$-functions. Furthermore we give an interpretation of quantum modularity at infinity for additive twists of $L$-functions of weight 2 cusp forms in terms of the corresponding functional equations.
184 - Trevor Hyde 2018
Let $M_{d,n}(q)$ denote the number of monic irreducible polynomials in $mathbb{F}_q[x_1, x_2, ldots , x_n]$ of degree $d$. We show that for a fixed degree $d$, the sequence $M_{d,n}(q)$ converges $q$-adically to an explicitly determined rational func tion $M_{d,infty}(q)$. Furthermore we show that the limit $M_{d,infty}(q)$ is related to the classic necklace polynomial $M_{d,1}(q)$ by an involutive functional equation, leading to a phenomenon we call liminal reciprocity. The limiting first moments of factorization statistics for squarefree polynomials are expressed in terms of a family of symmetric group representations as a consequence of liminal reciprocity.
68 - Xinrong Ma 2013
By virtue of Baileys well-known bilateral 6psi_6 summation formula and Watsons transformation formula,we extend the four-variable generalization of Ramanujans reciprocity theorem due to Andrews to a five-variable one. Some relevant new q-series ident ities including a new proof of Ramanujans reciprocity theorem and of Watsons quintuple product identity only based on Jacksons transformation are presented.
Assuming Schanuels conjecture, we prove that any polynomial exponential equation in one variable must have a solution that is transcendental over a given finitely generated field. With the help of some recent results in Diophantine geometry, we obtai n the result by proving (unconditionally) that certain polynomial exponential equations have only finitely many rational solutions. This answers affirmatively a question of David Marker, who asked, and proved in the case of algebraic coefficients, whether at least the one-variable case of Zilbers strong exponential-algebraic closedness conjecture can be reduced to Schanuels conjecture.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا