Multiplicative functions commutable with sums of squares
نویسندگان
چکیده
منابع مشابه
Multiplicative character sums with twice-differentiable functions
For a nontrivial multiplicative character χ modulo p, we bound character sums Sf (χ;N) = N ∑ n=1 χ(⌊f(n)⌋) taken on the integer parts of a real-valued, twice-differentiable function f whose second derivative decays at an appropriate rate. For the special case that f(x) = xη with some positive real number η, our bounds extend recent results of several authors. Mathematics Subject Classification ...
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We deduce asymptotic formulas for the alternating sums ∑ n≤x(−1)f(n) and ∑ n≤x(−1) 1 f(n) , where f is one of the following classical multiplicative arithmetic functions: Euler’s totient function, the Dedekind function, the sum-of-divisors function, the divisor function, the gcd-sum function. We also consider analogs of these functions, which are associated to unitary and exponential divisors, ...
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Let V be an affine algebraic variety over R (or any other real closed field R). We ask when it is true that every positive semidefinite (psd) polynomial function on V is a sum of squares (sos). We show that for dimV ≥ 3 the answer is always negative if V has a real point. Also, if V is a smooth non-rational curve all of whose points at infinity are real, the answer is again negative. The same h...
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2018
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s179304211850029x