ترغب بنشر مسار تعليمي؟ اضغط هنا

On the computation of Galois representations associated to level one modular forms

146   0   0.0 ( 0 )
 نشر من قبل Johan Bosman
 تاريخ النشر 2007
  مجال البحث
والبحث باللغة English
 تأليف Johan Bosman




اسأل ChatGPT حول البحث

In this paper we explicitly compute mod-l Galois representations associated to modular forms. To be precise, we look at cases with l<=23 and the modular forms considered will be cusp forms of level 1 and weight up to 22. We present the result in terms of polynomials associated to the projectivised representations. As an application, we will improve a known result on Lehmers non-vanishing conjecture for Ramanujans tau function.



قيم البحث

اقرأ أيضاً

We introduce Galois families of modular forms. They are a new kind of family coming from Galois representations of the absolute Galois groups of rational function fields over the rational field. We exhibit some examples and provide an infinite Galois family of non-liftable weight one Katz modular eigenforms over an algebraic closure of F_p for p in {3,5,7,11}.
158 - Johan Bosman 2011
For each of the groups PSL2(F25), PSL2(F32), PSL2(F49), PGL2(F25), and PGL2(F27), we display the first explicitly known polynomials over Q having that group as Galois group. Each polynomial is related to a Galois representation associated to a modula r form. We indicate how computations with modular Galois representations were used to obtain these polynomials. For each polynomial, we also indicate how to use Serres conjectures to determine the modular form giving rise to the related Galois representation.
We define L-functions for the class of real-analytic modular forms recently introduced by F. Brown. We establish their main properties and construct the analogue of period polynomial in cases of special interest, including those of modular iterated integrals.
192 - Yichao Zhang 2017
We establish an isomorphism between certain complex-valued and vector-valued modular form spaces of half-integral weight, generalizing the well-known isomorphism between modular forms for $Gamma_0(4)$ with Kohnens plus condition and modular forms for the Weil representation associated to the discriminant form for the lattice with Gram matrix $(2)$. With such an isomorphism, we prove the Zagier duality and write down the Borcherds lifts explicitly.
145 - Yichao Zhang 2013
In this note, we consider discriminant forms that are given by the norm form of real quadratic fields and their induced Weil representations. We prove that there exists an isomorphism between the space of vector-valued modular forms for the Weil repr esentations that are invariant under the action of the automorphism group and the space of scalar-valued modular forms that satisfy some epsilon-condition, with which we translate Borcherdss theorem of obstructions to scalar-valued modular forms. In the end, we consider an example in the case of level 12.
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