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Evaluate $L(1, \chi) = \sum_{n=1}^\infty \frac{\chi(n)}{n}$ for $\chi$ mod $3$

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#number-theory #solution-verification #analytic-number-theory #dirichlet-series #dirichlet-character
59
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Evaluate $L(1, \chi) = \sum_{n=1}^\infty \frac{\chi_5(n)}{n},$ for $\chi$ mod $5$

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#number-theory #solution-verification #analytic-number-theory #dirichlet-series #dirichlet-character
20
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What are trivial and non-trivial Dirichlet characters?

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#dirichlet-character
54
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"Mollifier" of the Dirichlet L-function

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#analytic-number-theory #riemann-zeta #zeta-functions #dirichlet-series #dirichlet-character
36
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What does $\sum_{p|n} \chi_{-4}(p)$ count?

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#sequences-and-series #number-theory #dirichlet-character
69
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Exponential Generating Function for Dirichlet Character

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#ordinary-differential-equations #number-theory #generating-functions #dirichlet-character
34
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Number of primitive Dirichlet characters of certain order and of bounded conductor

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#number-theory #elementary-number-theory #analytic-number-theory #arithmetic-functions #dirichlet-character
31
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Application of Dirichlet theorem and Dirchlet density

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#number-theory #algebraic-number-theory #dirichlet-character
53
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How to show that gcd of two quasiperiods is a quasiperiod?

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#elementary-number-theory #proof-explanation #modular-arithmetic #chinese-remainder-theorem #dirichlet-character
76
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Extending a Group Character to a Dirichlet Character

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#group-theory #characters #dirichlet-character
141
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Dirichlet Characters, Characteristic Functions, and Orthogonality in Proof of Dirichlet's Theorem

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#summation #proof-explanation #dirichlet-character
63
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Want to show $\sum_{n>N}n^{-1/2} \ll N^{-1/2}$

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#number-theory #analytic-number-theory #dirichlet-series #dirichlet-character
419
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Understanding sum of Dirichlet characters

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#number-theory #analytic-number-theory #dirichlet-character
207
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Calculate integral $ \int_{0}^{+\infty} \frac{x - \sin{\left(x \right)}}{x^{3}}\, dx $ using the Dirichlet integral

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#integration #improper-integrals #dirichlet-character
398
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Conductor of product of characters is the product of the conductors

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#number-theory #analytic-number-theory #dirichlet-character

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