Question

Uniform convergence about Dirichlet integral $f(s):=\int_1^\infty\frac{a(x)}{x^s}\,dx =\lim\limits_{T\to\infty}\int_1^T\frac{a(x)}{x^s}\,dx$

score 110 · Answer 1 · 2026-04-17 00:52:56

110

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Uniform convergence about Dirichlet integral $f(s):=\int_1^\infty\frac{a(x)}{x^s}\,dx =\lim\limits_{T\to\infty}\int_1^T\frac{a(x)}{x^s}\,dx$

Published on 17 Apr 2026 - 0:52

score 154 · Answer 2 · 2026-04-15 01:14:02

154

Views

If a subset of the primes has converging reciprocal sums, does it have relative density zero?

Published on 15 Apr 2026 - 1:14

score 81 · Answer 3 · 2026-04-12 10:27:11

81

Views

Does the Euler product for the Rankin-Selberg convolution of two eigenforms require the Ramanujan conjecture?

Published on 12 Apr 2026 - 10:27

score 63 · Answer 4 · 2026-04-14 09:55:55

63

Views

How fast does $\prod_{p\leq x}\frac 1{1-p^{-k}}$ diverge when $0<k<1$?

Published on 14 Apr 2026 - 9:55

score 94 · Answer 5 · 2026-04-16 21:13:44

94

Views

Show that $ \prod_{p \le x} \left(1-\frac{1}{p} \right)<\frac{1}{\ln{x}}$

Published on 16 Apr 2026 - 21:13

score 104 · Answer 6 · 2026-04-11 00:02:25

104

Views

Equality of contour integrals in Stein & Shakarchi's of Prime Number Theorem

Published on 11 Apr 2026 - 0:02

score 39 · Answer 7 · 2026-04-12 07:55:43

39

Views

Integral of mean square integral (coming from the circle method)

Published on 12 Apr 2026 - 7:55

score 84 · Answer 8 · 2026-04-14 07:37:00

84

Views

sum of square of cube function $r_3(n)$

Published on 14 Apr 2026 - 7:37

score 79 · Answer 9 · 2026-04-17 03:23:58

79

Views

Interchange of index in double summation -: $\sum_{n \leq x} \sum_{d | (n,K)} \mu(d) = \sum_{d | K} \sum_{n \leq x, d | n} \mu(d)$

Published on 17 Apr 2026 - 3:23

score 134 · Answer 10 · 2026-04-11 02:37:25

134

Views

Ineffectivness of constant in Siegel's theorem

Published on 11 Apr 2026 - 2:37

score 85 · Answer 11 · 2026-04-15 19:06:07

85

Views

Is the convergence of these two series equivalent? (They come from Khinchin's theorem and the Duffin-Schaeffer conjecture.)

Published on 15 Apr 2026 - 19:06

score 54 · Answer 12 · 2026-04-30 09:13:12

54

Views

How can I get more comfortable working with integrals and bounds in analytic number theory?

Published on 30 Apr 2026 - 9:13

score 87 · Answer 13 · 2026-04-12 08:28:37

87

Views

How to show the Kloosterman sum to be non zero?

Published on 12 Apr 2026 - 8:28

score 63 · Answer 14 · 2026-03-25 22:06:36

63

Views

$F=\{z\in\Bbb{H}:\ |z|>1,\ 2|\Re(z)|<\lambda\}$ is fundamental domain for $G_\lambda$(the subgroup of $SL(2,\Bbb{R})$ generated by $S$ and $T_\lambda$

Published on 25 Mar 2026 - 22:06

score 35 · Answer 15 · 2026-04-13 08:16:52

35

Views

Validity of Kusznetov's trace formula (which test functions are permissable)

Published on 13 Apr 2026 - 8:16

List Question

Uniform convergence about Dirichlet integral $f(s):=\int_1^\infty\frac{a(x)}{x^s}\,dx =\lim\limits_{T\to\infty}\int_1^T\frac{a(x)}{x^s}\,dx$

If a subset of the primes has converging reciprocal sums, does it have relative density zero?

Does the Euler product for the Rankin-Selberg convolution of two eigenforms require the Ramanujan conjecture?

How fast does $\prod_{p\leq x}\frac 1{1-p^{-k}}$ diverge when $0<k<1$?

Show that $ \prod_{p \le x} \left(1-\frac{1}{p} \right)<\frac{1}{\ln{x}}$

Equality of contour integrals in Stein & Shakarchi's of Prime Number Theorem

Integral of mean square integral (coming from the circle method)

sum of square of cube function $r_3(n)$

Interchange of index in double summation -: $\sum_{n \leq x} \sum_{d | (n,K)} \mu(d) = \sum_{d | K} \sum_{n \leq x, d | n} \mu(d)$

Ineffectivness of constant in Siegel's theorem

Is the convergence of these two series equivalent? (They come from Khinchin's theorem and the Duffin-Schaeffer conjecture.)

How can I get more comfortable working with integrals and bounds in analytic number theory?

How to show the Kloosterman sum to be non zero?

$F=\{z\in\Bbb{H}:\ |z|>1,\ 2|\Re(z)|<\lambda\}$ is fundamental domain for $G_\lambda$(the subgroup of $SL(2,\Bbb{R})$ generated by $S$ and $T_\lambda$

Validity of Kusznetov's trace formula (which test functions are permissable)

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