1,039 research outputs found
On the relation between p-adic and ordinary strings
The amplitudes for the tree-level scattering of the open string tachyons,
generalised to the field of p-adic numbers, define the p-adic string theory.
There is empirical evidence of its relation to the ordinary string theory in
the p_to_1 limit. We revisit this limit from a worldsheet perspective and argue
that it is naturally thought of as a continuum limit in the sense of the
renormalisation group.Comment: 13 pages harvmac (b), 2 eps figures; v2: revtex, shortened, published
versio
Non-vanishing of -functions associated to cusp forms of half-integral weight
In this article, we prove non-vanishing results for -functions associated
to holomorphic cusp forms of half-integral weight on average (over an
orthogonal basis of Hecke eigenforms). This extends a result of W. Kohnen to
forms of half-integral weight.Comment: 8 pages, Accepted for publication in Oman conference proceedings
(Springer
A Search for Instantons at HERA
A search for QCD instanton (I) induced events in deep-inelastic scattering
(DIS) at HERA is presented in the kinematic range of low x and low Q^2. After
cutting into three characteristic variables for I-induced events yielding a
maximum suppression of standard DIS background to the 0.1% level while still
preserving 10% of the I-induced events, 549 data events are found while
363^{+22}_{-26} (CDM) and 435^{+36}_{-22} (MEPS) standard DIS events are
expected. More events than expected by the standard DIS Monte Carlo models are
found in the data. However, the systematic uncertainty between the two
different models is of the order of the expected signal, so that a discovery of
instantons can not be claimed. An outlook is given on the prospect to search
for QCD instanton events using a discriminant based on range searching in the
kinematical region Q^2\gtrsim100\GeV^2 where the I-theory makes safer
predictions and the QCD Monte Carlos are expected to better describe the
inclusive data.Comment: Invited talk given at the Ringberg Workshop on HERA Physics on June
19th, 2001 on behalf of the H1 collaboratio
On pattern structures of the N-soliton solution of the discrete KP equation over a finite field
The existence and properties of coherent pattern in the multisoliton
solutions of the dKP equation over a finite field is investigated. To that end,
starting with an algebro-geometric construction over a finite field, we derive
a "travelling wave" formula for -soliton solutions in a finite field.
However, despite it having a form similar to its analogue in the complex field
case, the finite field solutions produce patterns essentially different from
those of classical interacting solitons.Comment: 12 pages, 3 figure
Factorizing Numbers with the Gauss Sum Technique: NMR Implementations
Several physics-based algorithms for factorizing large number were recently
published. A notable recent one by Schleich et al. uses Gauss sums for
distinguishing between factors and non-factors. We demonstrate two NMR
techniques that evaluate Gauss sums and thus implement their algorithm. The
first one is based on differential excitation of a single spin magnetization by
a cascade of RF pulses. The second method is based on spatial averaging and
selective refocusing of magnetization for Gauss sums corresponding to factors.
All factors of 16637 and 52882363 are successfully obtained.Comment: 4 pages, 4 figures; Abstract and Conclusion are slightly modified.
References added and formatted with Bibte
Detecting brute-force attacks on cryptocurrency wallets
Blockchain is a distributed ledger, which is protected against malicious
modifications by means of cryptographic tools, e.g. digital signatures and hash
functions. One of the most prominent applications of blockchains is
cryptocurrencies, such as Bitcoin. In this work, we consider a particular
attack on wallets for collecting assets in a cryptocurrency network based on
brute-force search attacks. Using Bitcoin as an example, we demonstrate that if
the attack is implemented successfully, a legitimate user is able to prove that
fact of this attack with a high probability. We also consider two options for
modification of existing cryptocurrency protocols for dealing with this type of
attacks. First, we discuss a modification that requires introducing changes in
the Bitcoin protocol and allows diminishing the motivation to attack wallets.
Second, an alternative option is the construction of special smart-contracts,
which reward the users for providing evidence of the brute-force attack. The
execution of this smart-contract can work as an automatic alarm that the
employed cryptographic mechanisms, and (particularly) hash functions, have an
evident vulnerability.Comment: 10 pages, 2 figures; published versio
On rationality of the intersection points of a line with a plane quartic
We study the rationality of the intersection points of certain lines and
smooth plane quartics C defined over F_q. For q \geq 127, we prove the
existence of a line such that the intersection points with C are all rational.
Using another approach, we further prove the existence of a tangent line with
the same property as soon as the characteristic of F_q is different from 2 and
q \geq 66^2+1. Finally, we study the probability of the existence of a rational
flex on C and exhibit a curious behavior when the characteristic of F_q is
equal to 3.Comment: 17 pages. Theorem 2 now includes the characteristic 2 case;
Conjecture 1 from the previous version is proved wron
Gauss sum factorization with cold atoms
We report the first implementation of a Gauss sum factorization algorithm by
an internal state Ramsey interferometer using cold atoms. A sequence of
appropriately designed light pulses interacts with an ensemble of cold rubidium
atoms. The final population in the involved atomic levels determines a Gauss
sum. With this technique we factor the number N=263193.Comment: 4 pages, 5 figure
Integral representations of q-analogues of the Hurwitz zeta function
Two integral representations of q-analogues of the Hurwitz zeta function are
established. Each integral representation allows us to obtain an analytic
continuation including also a full description of poles and special values at
non-positive integers of the q-analogue of the Hurwitz zeta function, and to
study the classical limit of this q-analogue. All the discussion developed here
is entirely different from the previous work in [4]Comment: 14 page
- …