Results 31 to 40 of about 9,690 (225)
New estimates for exponential sums over multiplicative subgroups and intervals in prime fields [PDF]
Journal of Number Theory, 2020 Let ${\mathcal H}$ be a multiplicative subgroup of $\mathbb{F}_p^*$ of order $H>p^{1/4}$. We show that $$ \max_{(a,p)=1}\left|\sum_{x\in {\mathcal H}} {\mathbf{\,e}}_p(ax)\right| \le H^{1-31/2880+o(1)}, $$ where ${\mathbf{\,e}}_p(z) = \exp(2 i z/p)$, which improves a result of Bourgain and Garaev (2009).
Daniel Di Benedetto +5 more
openaire +2 more sources
Explicit relations between primes in short intervals and exponential sums over primes [PDF]
Functiones et Approximatio Commentarii Mathematici, 2014 one reference ...
LANGUASCO, ALESSANDRO, A. Zaccagnini
openaire +4 more sources
Almost all primes have a multiple of small Hamming weight
, 2016 Recent results of Bourgain and Shparlinski imply that for almost all primes $p$ there is a multiple $mp$ that can be written in binary as $mp= 1+2^{m_1}+ \cdots +2^{m_k}, \quad 1\leq m_1 < \cdots < m_k,$ with $k=66$ or $k=16$, respectively. We show that $
Elsholtz, Christian
core +1 more source
Multiple Exponential and Character Sums with Monomials
, 2013 We obtain new bounds of multivariate exponential sums with monomials, when the variables run over rather short intervals. Furthermore, we use the same method to derive estimates on similar sums with multiplicative characters to which previously known ...
Shparlinski, Igor
core +1 more source
FEBS Letters, EarlyView.The Ile181Asn variant of human UDP‐xylose synthase (hUXS1), associated with a short‐stature genetic syndrome, has previously been reported as inactive. Our findings demonstrate that Ile181Asn‐hUXS1 retains catalytic activity similar to the wild‐type but exhibits reduced stability, a looser oligomeric state, and an increased tendency to precipitate ...
Tuo Li +2 more
wiley +1 more source
On Some Dynamical Systems in Finite Fields and Residue Rings
, 2007 We use character sums to confirm several recent conjectures of V. I. Arnold on the uniformity of distribution properties of a certain dynamical system in a finite field. On the other hand, we show that some conjectures are wrong.
Shparlinski, Igor E.
core +1 more source
FEBS Letters, EarlyView.We reconstituted Synechocystis glycogen synthesis in vitro from purified enzymes and showed that two GlgA isoenzymes produce glycogen with different architectures: GlgA1 yields denser, highly branched glycogen, whereas GlgA2 synthesizes longer, less‐branched chains.
Kenric Lee +3 more
wiley +1 more source
EXPONENTIAL SUMS OVER POINTS OF ELLIPTIC CURVES WITH RECIPROCALS OF PRIMES [PDF]
, 2017 We consider exponential sums with x-coordinates of points qG and q−1G where G is a point of order T on an elliptic curve modulo a prime p and q runs through all primes up toN (with gcd (q,T)=1 in the case of the points q−1G).
Ostafe, Alina, Shparlinski, Igor E.
core
Fermat quotients: Exponential sums, value set and primitive roots
, 2011 For a prime $p$ and an integer $u$ with $\gcd(u,p)=1$, we define Fermat quotients by the conditions $$ q_p(u) \equiv \frac{u^{p-1} -1}{p} \pmod p, \qquad 0 \le q_p(u) \le p-1. $$ D. R.
Shparlinski, Igor E.
core +1 more source
Molecular Oncology, EarlyView.Pharmacologic ascorbate (vitamin C) increases ROS, disrupts cellular metabolism, and induces DNA damage in CRPC cells. These effects sensitize tumors to PARP inhibition, producing synergistic growth suppression with olaparib in vitro and significantly delayed tumor progression in vivo. Pyruvate rescue confirms ROS‐dependent activity.
Nicolas Gordon +13 more
wiley +1 more source