Results 11 to 20 of about 261 (203)
On exponential sums over prime numbers [PDF]
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1989 AbstractIn this article we establish an estimate for a sum over primes that is the analogue of an estimate for a sum over consecutive integers which has proved to be very useful in applications of exponential sums to problems in number theory.
Sárközy, A., Stewart, C. L.
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Explicit upper bounds for exponential sums over primes [PDF]
Mathematics of Computation, 2000 We give explicit upper bounds for linear trigonometric sums over primes.
Daboussi, Hedi, Rivat, Joel
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Exponential sums over primes in an arithmetic progression [PDF]
Proceedings of the American Mathematical Society, 1985 In 1979 A. F. Lavrik obtained some estimates for exponential sums over primes in arithmetic progressions by an analytic method. In the present paper we give an estimate for the same sums, comparable with Lavrik’s estimate, by means of elementary methods like Vaughan’s identity.
A. BALOG, PERELLI, ALBERTO
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On certain exponential sums over primes
Journal of Number Theory, 2009 Let \(f(x)\) be a real valued polynomial of degree \(k\geq 4\) and irrational leading coefficient \(\alpha\). Exponential sums of the form \[ S:=\sum_{p\leq N} (\log p) e(f(p)) \] have received a lot of interest. \textit{G. Harman} proved in [Mathematika 28, 249--254 (1981; Zbl 0465.10029)] that if \(q\) is the denominator of a convergent of \(\alpha\),
Maier, H., Sankaranarayanan, A.
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Exponential sum estimates over prime fields [PDF]
International Journal of Number Theory, 2019 In this paper, we prove some extensions of recent results given by Shkredov and Shparlinski on multiple character sums for some general families of polynomials over prime fields. The energies of polynomials in two and three variables are our main ingredients.
Koh, Doowon +3 more
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EXPONENTIAL SUMS OVER POINTS OF ELLIPTIC CURVES WITH RECIPROCALS OF PRIMES [PDF]
Mathematika, 2011 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). We obtain a new bound on exponential sums with q−1G and correct an imprecision in the work of W.D. Banks, J.B. Friedlander, M.Z.
Ostafe, Alina, Shparlinski, Igor E
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Repairing Reed-Solomon Codes Over Prime Fields via Exponential Sums
IEEE Transactions on Information Theory, 2023 This paper presents two repair schemes for low-rate Reed-Solomon (RS) codes over prime fields that can repair any node by downloading a constant number of bits from each surviving node. The total bandwidth resulting from these schemes is greater than that incurred during trivial repair; however, this is particularly relevant in the context of leakage ...
Roni Con +3 more
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Real exponential sums over primes and prime gaps
, 2023 27 pages, submitted to Annals of ...
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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 ${\mathbf{\,e}}_p(z) = \exp(2 πi z/p)$, which improves a result of Bourgain and Garaev (2009).
Daniel Di Benedetto +5 more
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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
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