Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA Note About the {Ki(z)} Functions
ملاحظة حول وظائف {Ki(z)}
109
0
0.0
(
0
)
Authors
Branko J. Malesevic
Ask ChatGPT about the research
في المقالة [بيتويفيتش 2006]، أثبت آ. بيتويفيتش خصائص مفيدة لأساليب $K_{i}(z)$ التي تجريد دالة الجهة اليسرى لكوريبا [Kurepa 1971]. في هذه الملاحظة، نقدم إثباتات مبسطة لأثنين من هذه النتائج، ونجيب على السؤال المفتوح الذي تم ذكره في [بيتويفيتش 2006]. وأخيرا، نناقش الخلوية التطورية لأساليب $K_{i}(z)$.
In the article [Petojevic 2006], A. Petojevi c verified useful properties of the $K_{i}(z)$ functions which generalize Kurepas [Kurepa 1971] left factorial function. In this note, we present simplified proofs of two of these results and we answer the open question stated in [Petojevic 2006]. Finally, we discuss the differential transcendency of the $K_{i}(z)$ functions.
rate research
Read More
We prove that if f and g are holomorphic functions on an open connected domain, with the same moduli on two intersecting segments, then f = g up to the multiplication of a unimodular constant, provided the segments make an angle that is an irrational multiple of $pi$. We also prove that if f and g are functions in the Nevanlinna class, and if |f | = |g| on the unit circle and on a circle inside the unit disc, then f = g up to the multiplication of a unimodular constant.
We study the adjunction property of the Jacquet-Emerton functor in certain neighborhoods of critical points in the eigencurve. As an application, we construct two-variable $p$-adic $L$-functions around critical points via Emertons representation theoretic approach.
We define generalised zeta functions associated to indefinite quadratic forms of signature (g-1,1) -- and more generally, to complex symmetric matrices whose imaginary part has signature (g-1,1) -- and we investigate their properties. These indefinite zeta functions are defined as Mellin transforms of indefinite theta functions in the sense of Zwegers, which are in turn generalised to the Siegel modular setting. We prove an analytic continuation and functional equation for indefinite zeta functions. We also show that indefinite zeta functions in dimension 2 specialise to differences of ray class zeta functions of real quadratic fields, whose leading Taylor coefficients at s=0 are predicted to be logarithms of algebraic units by the Stark conjectures.
A generalized Riemann hypothesis states that all zeros of the completed Hecke $L$-function $L^*(f,s)$ of a normalized Hecke eigenform $f$ on the full modular group should lie on the vertical line $Re(s)=frac{k}{2}.$ It was shown by Kohnen that there exists a Hecke eigenform $f$ of weight $k$ such that $L^*(f,s) eq 0$ for sufficiently large $k$ and any point on the line segments $Im(s)=t_0, frac{k-1}{2} < Re(s) < frac{k}{2}-epsilon, frac{k }{2}+epsilon < Re(s) < frac{k+1}{2},$ for any given real number $t_0$ and a positive real number $epsilon.$ This paper concerns the non-vanishing of the product $L^*(f,s)L^*(f,w)$ $(s,win mathbb{C})$ on average.
We generalize Bangerts non-hyperbolicity result for uniformly tamed almost complex structures on standard symplectic $R^{2n}$ to asymtotically standard symplectic manifolds.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
