Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Prime solutions to polynomial equations in many variables and differing
  degrees   Let $\mathbf{f} = (f_1, \ldots, f_R)$ be a system of polynomials with integer
coefficients in which the degrees need not all be the same. We provide
sufficient conditions for which the system of equations $f_j (x_1, \ldots, x_n)
= 0 \ (1 \leq j \leq R)$ satisfies a general local to global type statement,
and has a solution where each coordinate is prime. In fact we obtain the
asymptotic formula for number of such solutions, counted with a logarithmic
weight, under these conditions. We prove the statement via the Hardy-Littlewood
circle method. This is a generalization of the work of B. Cook and \'{A}.
Magyar, where they obtained the result when the polynomials of $\mathbf{f}$ all
have the same degree. Hitherto, results of this type for systems of polynomial
equations involving different degrees have been restricted to the diagonal
case.

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The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas