اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn a linear form for Catalans constant
173
0
0.0
(
0
)
تأليف
Christian Krattenthaler
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
It is shown how Andrews multidimensional extension of Watsons transformation between a very-well-poised $_8phi_7$-series and a balanced $_4phi_3$-series can be used to give a straightforward proof of a conjecture of Zudilin and the second author on the arithmetic behaviour of the coefficients of certain linear forms of 1 and Catalans constant. This proof is considerably simpler and more stream-lined than the first proof, due to the second author.
قيم البحث
اقرأ أيضاً
In 1947 Mills proved that there exists a constant $A$ such that $lfloor A^{3^n} rfloor$ is a prime for every positive integer $n$. Determining $A$ requires determining an effective Hoheisel type result on the primes in short intervals - though most b
ooks ignore this difficulty. Under the Riemann Hypothesis, we show that there exists at least one prime between every pair of consecutive cubes and determine (given RH) that the least possible value of Mills constant $A$ does begin with 1.3063778838. We calculate this value to 6850 decimal places by determining the associated primes to over 6000 digits and probable primes (PRPs) to over 60000 digits. We also apply the Cramer-Granville Conjecture to Honakers problem in a related context.
We show that if a rational map is constant on each isomorphism class of unpolarized abelian varieties of a given dimension, then it is a constant map. Our results are motivated by and shed light on a proposed construction of a cryptographic protocol for multiparty non-interactive key exchange.
Let F be a global field and A its ring of adeles. Let G:=SL(2). We study the bilinear form B on the space of K-finite smooth compactly supported functions on G(A )/G(F) defined by the formula B (f,g):=B(f,g)-(M^{-1}CT (f),CT (g)), where B is the usua
l scalar product, CT is the constant term operator, and M is the standard intertwiner. This form is natural from the viewpoint of the geometric Langlands program. To justify this claim, we provide a dictionary between the classical and geometric theory of automorphic forms. We also show that the form B is related to S. Schieders Picard-Lefschetz oscillators.
We investigate arithmetic properties of values of the entire function $$ F(z)=F_q(z;lambda)=sum_{n=0}^inftyfrac{z^n}{prod_{j=1}^n(q^j-lambda)}, qquad |q|>1, quad lambda otin q^{mathbb Z_{>0}}, $$ that includes as special cases the Tschakaloff functio
n ($lambda=0$) and the $q$-exponential function ($lambda=1$). In particular, we prove the non-quadraticity of the numbers $F_q(alpha;lambda)$ for integral $q$, rational $lambda$ and $alpha otin-lambda q^{mathbb Z_{>0}}$, $alpha e0$.
Let $E$ be an elliptic curve, with identity $O$, and let $C$ be a cyclic subgroup of odd order $N$, over an algebraically closed field $k$ with $operatorname{char} k mid N$. For $P in C$, let $s_P$ be a rational function with divisor $N cdot P - N c
dot O$. We ask whether the $N$ functions $s_P$ are linearly independent. For generic $(E,C)$, we prove that the answer is yes. We bound the number of exceptional $(E,C)$ when $N$ is a prime by using the geometry of the universal generalized elliptic curve over $X_1(N)$. The problem can be recast in terms of sections of an arbitrary degree $N$ line bundle on $E$.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
