The prime ideals in every class contain arbitrary large truncated classes
We prove that the prime ideals in every class of a number field contain arbitrary large truncated ideal classes.
math.NT↗
arXiv subjects
Chunlei Liu
Publications and source records attributed to Chunlei Liu.
Review of D Semi-leptonic Decays
Semi-leptonic D decays continue to play an important role in the field of flavor physics. During this presentation, recent measurements from pseudo-scalar to pseudo-scalar modes, pseudo-scalar to vector modes, and rare modes will be discussed. These results are important for many purposes, such as validating the machinery of lattice QCD, extracting CKM matrix elements, and searching for new physics and new interactions.
hep-ex↗
A sup-Hodge bound for exponential sums
The $C$-function of $T$-adic exponential sums is studeid. An explicit arithmetic bound is established for the Newton polygon of the $C$-function. This polygon lies above the Hodge polygon. It gives a sup-Hodge bound of the $C$-function of $p$-power order exponential sums.
math.NT↗
Twisted exponential sums of polynomials in one variable
The twisted $T$-adic exponential sum associated to a polynomial in one variable is studied. An explicit arithmetic polygon in terms of the highest two exponents of the polynomial is proved to be a lower bound of the Newton polygon of the $C$-function of the twisted T-adic exponential sum. This bound gives lower bounds for the Newton polygon of the $L$-function of twisted $p$-power order exponential sums.
math.NT↗
Generic twisted $T$-adic exponential sums of polynomials
The twisted $T$-adic exponential sum associated to a polynomial in one variable is studied. An explicit arithmetic polygon is proved to be the generic Newton polygon of the twisted $C$-function of the T-adic exponential sum. It gives the generic Newton polygon of the twisted $L$-functions of $p^m$-power order exponential sums, for all $m$.
math.NT↗
Generic twisted $T$-adic exponential sums of binomials
The twisted $T$-adic exponential sum associated to $x^{d}+λx$ is studied. If $λ\neq0,$ then an explicit arithmetic polygon is proved to be the Newton polygon of the twisted $C$-function of the T-adic exponential sum. It gives the Newton polygons of the $L$-functions of twisted $p$-power order exponential sums.
math.NT↗
Generic T-adic exponential sums in one variable
The $T$-adic exponential sum associated to a Laurent polynomial in one variable is studied. An explicit arithmetic polygon is proved to be the generic Newton polygon of the $C$-function of the T-adic exponential sum. It gives the generic Newton polygon of $L$-functions of $p$-power order exponential sums.
math.NT↗
$T$-adic exponential sums of polynomials in one variable
The $T$-adic exponential sum of a polynomial in one variable is studied. An explicit arithmetic polygon in terms of the highest two exponents of the polynomial is proved to be a lower bound of the Newton polygon of the $C$-function of the T-adic exponential sum. This bound gives lower bounds for the Newton polygon of the $L$-function of exponential sums of $p$-power order.
math.NT↗
T-adic exponential sums under diagonal base change
Twistec T-adic exponential sums are studied. As an application, the behavior of the L-function under diagonal base chang is explicitely given.
math.NT↗
T-adic exponential sums over finite fields
$T$-adic exponential sums associated to a Laurent polynomial $f$ are introduced. They interpolate all classical $p^m$-power order exponential sums associated to $f$. The Hodge bound for the Newton polygon of $L$-functions of $T$-adic exponential sums is established. This bound enables us to determine, for all $m$, the Newton polygons of $L$-functions of $p^m$-power order exponential sums associated to an $f$ which is ordinary for $m=1$. Deeper properties of $L$-functions of $T$-adic exponential sums are also studied. Along the way, new open problems about the $T$-adic exponential sum itself are discussed.
math.NT↗
Generic exponential sums associated to Laurent polynomials in one variable
Generic Newton polygons for L-functions of exponential sums associated to Laurent polynomials in one variable are determined. The corresponding Hasse polynomials are also determined.
math.NT↗
Search for CP Violation in B0s to J/psi phi at CDF
The CKM mechanism is well established as the dominant mechanism for $CP$ violation, which was first discovered in the neutral kaons in 1964 \cite{ref:cpkaon}. To search for new sources of CP violation, one can exploit a handful of systems in which the standard model makes a precise prediction of CP violation. In the $B^0_s\to J/ψϕ$ system, CP violation in the interference of mixing and decay is precisely predicted in the standard model, the prediction being very close to zero. The CDF experiment reconstructs about 2000 signal events in 1.35 fb$^{-1}$ of luminosity. We obtain a confidence region in the space of the parameters $β_s$, the CP phase, and $ΔΓ$, the width difference. This result is 1.5 $σ$ from the standard model prediction.
hep-ex↗
Recent Lifetime and Mixing Measurements at the Tevatron
We present the latest $B$ hadron lifetimes, $B^0_s$ mixing, and $D^0$ mixing measurements using up to 3.0 fb$^{-1}$ of data collected by CDF and D0 experiments at Fermilab. The $B^0_s$ lifetime is measured from both $J/ψϕ$ (CP admixture) and flavor specific channels, and the $B_c$ lifetime is obtained from semileptonic channels. Following the $B^0_s$ oscillation frequency measurement at CDF in 2006, the D0 collaboration now observes $B^0_s$ oscillation at a significance of about 3$σ$. Since the first $D^0$ mixing evidence established at $B$ factories in 2007, CDF has observed $D^0$ mixing at a significance of about 4$σ$ level, the first time from hadron collider.
hep-ex↗
Arithmetic progressions of primes in short intervals
Green and Tao proved that the primes contains arbitrarily long arithmetic progressions. We show that, essentially the same proof leads to the following result: The primes in an short interval contains many arithmetic progressions of any given length.
math.NT↗
Sublattices of finite index
Assuming the Gowers Inverse conjecture and the Möbius conjecture for the finite parameter $s$, Green-Tao verified Dickson's conjecture for lattices which are ranges of linear maps of complexity at most $s$. In this paper, we reformulate Green-Tao's theorem on Dickson's conjecture, and prove that, if $L$ is the range of a linear map of complexity $s$, and $L_1$ is a sublattice of $L$ of finite index, then $L_1$ is the range of a linear map of complexity $s$.
math.NT↗
The L-functions of twisted Witt extensions
The L-function of a non-degenerate twisted Witt extension is proved to be a polynomial. Its Newton polygon is proved to lie above the Hodge polygon of that extension. And the Newton polygons of the Gauss-Heilbronn sums are explicitly determined, generalizing the Stickelberger theorem.
math.NT↗
The $L$-functions of Witt coverings
Results on $L$-functions of Artin-Schreier coverings by Dwork, Bombieri and Adolphson-Sperber are generalized to $L$-functions of Witt coverings.
math.NT↗
The critical order of certain Hecke L-functions of imaginary quadratic fields
Let $-D < -4$ denote a fundamental discriminant which is either odd or divisible by 8, so that the canonical Hecke character of $\Bbb Q(\sqrt{-D})$ exists. Let $d$ be a fundamental discriminant prime to $D$. Let $2k-1$ be an odd natural integer prime to the class number of $\Bbb Q(\sqrt{-D})$. Let $χ$ be the twist of the $(2k-1)$th power of a canonical Hecke character of $\Bbb Q(\sqrt{-D})$ by the Kronecker's symbol $n\mapsto(\frac{d}{n})$. It is proved that the order of the Hecke $L$-function $L(s,χ)$ at its central point $s=k$ is determined by its root number when $|d| \leq c(ε)D^{{1/24}-ε}$ or, when $|d| \leq c(ε)D^{\frac1{12} -ε}$ and $k\geq 2$, where $ε> 0$ and $c(ε)$ is a constant depending only on $ε$.
math.NT↗