Exponential sums over cubes of primes in short intervals and its applications
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DOI: 10.1007/s00209-020-02649-8
Abstract: In this paper, we treat the estimate on exponential sums over cubes of primes in short intervals, and improve a previous bound of Kumchev (in: Number Theory: Arithmetic in Shangri-La (Proc. China-Japan Seminar Number Theory),… read more here.
Keywords: exponential sums; cubes primes; sums cubes; intervals applications ... See more keywords
Higher integral moments of automorphic L-functions in short intervals
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DOI: 10.1016/j.jnt.2016.07.004
Abstract: We consider the higher integral moments for automorphic L-functions in short intervals and give a proof for the conjecture of Conrey et al. under Generalized Riemann Hypothesis for automorphic L-function. read more here.
Keywords: functions short; integral moments; automorphic functions; moments automorphic ... See more keywords
Frobenius distributions in short intervals for CM elliptic curves
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DOI: 10.1016/j.jnt.2018.01.007
Abstract: Abstract For an elliptic curve E / Q , Hasse's theorem asserts that # E ( F p ) = p + 1 − a p , where | a p | ≤ 2 p… read more here.
Keywords: frobenius distributions; elliptic curves; distributions short; short intervals ... See more keywords
Universality of the Riemann zeta-function in short intervals
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DOI: 10.1016/j.jnt.2019.04.006
Abstract: Abstract By the Voronin theorem, the set of shifts of the Riemann zeta-function ζ ( s + i τ ) , s = σ + i t , τ ∈ R , that approximate any… read more here.
Keywords: function short; zeta function; universality riemann; riemann zeta ... See more keywords
Cyclicity and exponents of CM elliptic curves modulo $p$ in short intervals
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DOI: 10.1090/tran/8197
Abstract: Let E be a CM elliptic curve defined over Q. We establish an asymptotic formula for the number of primes p for which the reduction modulo p of E is cyclic over short intervals. This… read more here.
Keywords: exponents elliptic; cyclicity exponents; elliptic curves; short intervals ... See more keywords
Bombieri-type theorems of nonlinear Weyl sums over primes in short intervals
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DOI: 10.1142/s1793042118501531
Abstract: In this paper, we consider the mean-value estimate for nonlinear Weyl sums over primes in short intervals and establish the related Bombieri-type theorems. These results have applications in additive problems with prime variables in short… read more here.
Keywords: nonlinear weyl; sums primes; bombieri type; short intervals ... See more keywords
On triple correlations of Fourier coefficients of cusp forms. II
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DOI: 10.1142/s1793042119500374
Abstract: The triple correlation [Formula: see text] for arbitrary coefficients [Formula: see text] is estimated on average over [Formula: see text] in some short intervals. By introducing a device of short intervals, we are able to… read more here.
Keywords: see text; formula see; cusp forms; short intervals ... See more keywords