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3 questions
6
votes
0
answers
654
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Generalized prime number theorem and Riemann Hypothesis for non-number math objects
My question is about some math objects (matrices, polynomials) and operators that satisfy a number of properties which can lead to a theory similar to PNT, RH, Dirichlet functions, abscissa of ...
- 3,098
2
votes
1
answer
186
views
Existence of analytic continuation of Dirichlet series corresponding to the indicator sequence of a complement of a special multiplicative set
Let $K/ \mathbb Q $ be a finite Galois extension and let $X$ be a proper non-empty subset of the Galois group $G=Gal(K/ \mathbb Q)$ that is closed under conjugation. Consider a set of integer primes $...
- 21.3k
4
votes
1
answer
448
views
The sign of an interesting sum involving a Dirichlet character
Let $\chi_{q}$ be a primitive Dirichlet character with modulus $q$ (see definition at wikipedia ).
For example for $q=5$ we have
\begin{equation}
\begin{aligned}
\chi_{5,1}&=(1, 1, 1, 1, 0),\\
...
- 105k