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Why does the divisor-counting function appear in bounds for Kloosterman sums?

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#analytic-number-theory #arithmetic-functions #multiplicative-function
35
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Show $\sum_{c|n} \mu(c)f(c) = \{1-f(p_1)\}\{1-f(p_2)\} \dots \{1-f(p_r)\}$

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#number-theory #elementary-number-theory #multiplicative-function
292
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Sum of divisors function inequality

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#elementary-number-theory #multiplicative-function
186
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find all $n$ such that $\varphi(\sigma(2^n)) = 2^n$

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#elementary-number-theory #multiplicative-function
67
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Prove of $\prod_{d|n} (\mu(d)(\mu(d) + 3) + 4) = 4^{d(n)}$

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#number-theory #products #mobius-function #multiplicative-function
1.1k
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Is $\sum_{d | n} f(d)$ completely multiplicative if $f$ is completely multiplicative?

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#number-theory #multiplicative-function
78
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Uniqueness of $f( x y - 1) = f(x-1)f(y-1),f(1) = A,f(1+n)>f(n)$?

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#computational-complexity #functional-equations #multiplicative-function
143
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Optimal multiplying method

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#polynomials #arithmetic #computational-complexity #multiplicative-function
73
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Infinite Product for Multiplicative Functions

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#reference-request #closed-form #infinite-product #multiplicative-function
8.9k
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The sigma function (sum of divisors) multiplicative proof

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#elementary-number-theory #prime-numbers #divisor-sum #multiplicative-function
66
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What is the largest (if any) multiplicative modulo group with all prime elements?

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#finite-groups #modular-arithmetic #cyclic-groups #multiplicative-function
468
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Does the Mobius Inversion Theorem hold when sum function is over multiples instead of divisors

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#number-theory #arithmetic-functions #multiplicative-function #mobius-function
1.7k
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Show that $f(n) = \gcd(a,n)$ is a multiplicative function

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#elementary-number-theory #gcd-and-lcm #multiplicative-function
1.5k
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Formula for square of the number of divisors $\sum_{r\mid n} d(r^2) = d^2(n)$

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#summation #analytic-number-theory #arithmetic-functions #multiplicative-function #divisor-counting-function
48
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Is there any way to simplify this function?

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#number-theory #multiplicative-function

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