A beautiful blending of real/complex analysis with number theory. The study involves distribution of prime numbers and other problems and helps giving asymptotic estimates to these.

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### Is the de Bruijn-Newman constant non-positive?

**5**

**2**answers

### asymptotic for li(x)-Ri(x)

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### How to prove a Mersenne number is not pseudoprime to the base 3?

**1**

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### Counting "simultaneous squares' over the Gaussian integers

**3**

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### Modular root of $-1$

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**1**answer

### Parity and number of squares taken by polynomials in a range?

**-4**

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### About a pattern on prime numbers [on hold]

**11**

**1**answer

### Partial product of Euler factors

**8**

**1**answer

### Are there infinitely many primes of this form?

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### Infinite difference length of integer subsets

**2**

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### Twisted modular equation

**1**

**1**answer

### Sum of log over friables

**2**

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### Expressing modular functions of level 9 and 32 as rational functions

**3**

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### Analytic continuation of a Dirichlet series with several complex variables

**5**

**1**answer

### An asymptotic formula for this sum

**7**

**1**answer

### Goldbach's conjecture for the Liouville function

**3**

**1**answer

### Number of $k$-free integers of bounded radical

**-1**

**0**answers

### Deuring-Heilbronn phenomenon: would a lower bound of $\lambda/\mu$ imply GRH?

**4**

**1**answer

### The number of solutions of the equation $ax_1x_2+by_1y_2=n$

**10**

**1**answer

### How many zeta zeros are needed to accurately calculate five digits for π(1000000), where π(x) is the prime counting function?

**10**

**1**answer

### Why are the coefficients of the modular equation so large?

**34**

**5**answers

### “Long-standing conjectures in analysis … often turn out to be false”

**11**

**2**answers

### Equidistribution of CM points in the principal genus

**3**

**1**answer

### On the Dirichlet series for $1/\zeta(s)$ at $\Re(s)=1/2$

**-2**

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### Left-right discrepancy in a short interval containing k0 primes

**1**

**2**answers

### Number theory on Banach space $L^2(\mathbb R)$ meets linear independence?

**0**

**0**answers

### Summation formula for twisted L-function

**10**

**1**answer

### Spacing of fractions with prime denominator

**9**

**0**answers

### The trace formula over function fields

**4**

**1**answer

### Is there some numerical evidence that $ \pi(x+x^{1/e})-\pi(x)\geq 1 $ for any large enough $ x $?

**3**

**0**answers

### Cancellation in this exponential sum?

**1**

**1**answer

### zeros of sums of complex exponential functions

**0**

**4**answers

### On the real part of the Riemann zeta function inside the critical strip

**1**

**1**answer

### On a certain integral representation for Dirichlet L-functions

**4**

**2**answers

### Is Riemann zeta function injective in some strips $a<\Re(s)<b$, where $0\leq a<b \leq 1$?

**1**

**0**answers

### Fejer-Jackson-like inequality with divisor sum

**0**

**1**answer

### Is $P_{2n} \ge 2P_n$ and $\pi(2x) \le 2\pi(x)$ inconsistent to the Prime k-tuple conjecture?

**25**

**1**answer

### Lindelöf hypothesis claim

**3**

**0**answers

### Why is the smallest (fractional) absolute central moment of a Gaussian distribution almost at $\sqrt{3}/2$?

**0**

**1**answer

### Sergei numbers : even integers n being a prime gap at least n times

**-3**

**1**answer

### Can this weakening of Polignac's conjecture be proven?

**12**

**2**answers

### Is every odd positive integer of the form $P_{n+m}-P_n-P_m$?

**-1**

**1**answer

### Explicit second order bounds for the prime counting function

**5**

**1**answer

### Prove: If $P_n$ is $n$-$th$ prime number then $P_{n+m} \ge P_n+P_m$

**3**

**1**answer

### The Gauss Circle Problem asymptotic in dimension

**5**

**2**answers

### $\pi((n+1)^2)-\pi(n^2) \le \pi(n)$ for all $n \ge 370$?

**4**

**1**answer

### 3-smooth number

**3**

**1**answer

### Sum of Legendre symbol over primes

**2**

**0**answers

### Dirichlet series as rational zeta expressions

**23**

**0**answers