Sums of two squares are strongly biased towards quadratic residues

DOI10.2140/ant.2023.17.775OpenAlexW3216718214MaRDI QIDQ2699292

Ofir Gorodetsky

Publication date: 26 April 2023

Published in: Algebra \& Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.12662

zbMATH Keywords

Chebyshev's biasomega functionprime divisor functionsums of two squares

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) (zeta (s)) and (L(s, chi)) (11M06)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Highly biased prime number races
• Real zeros of quadratic Dirichlet \(L\)-functions
• Nonvanishing of quadratic Dirichlet \(L\)-functions at \(s=\frac{1}{2}\)
• Chebyshev's bias in dihedral and generalized quaternion Galois groups
• Lemke Oliver and Soundararajan bias for consecutive sums of two squares
• Chebyshev's bias for products of irreducible polynomials
• Chebyshev's bias for products of \(k\) primes
• BIG BIASES AMONGST PRODUCTS OF TWO PRIMES
• Chebyshev's Bias for Products of Two Primes
• OSCILLATORY PROPERTIES OF REAL FUNCTIONS WITH WEAKLY BOUNDED MELLIN TRANSFORM
• Elliptic Curves of Unbounded Rank and Chebyshev's Bias
• Prime number races for elliptic curves over function fields
• Numerical Computations Concerning the ERH
• Chebyshev’s bias in function fields
• Comparative prime-number theory. I
• Some problems of analytic number theory
• The half dimensional sieve
• Chebyshev’s bias for composite numbers with restricted prime divisors
• Chebyshev's Bias
• ON THE DISTRIBUTION OF PRIMES (mod4)
• Chebyshev’s bias for analyticL-functions
• The variance of the number of sums of two squares in [inline-graphic 01 [T] in short intervals]
• NUMBER OF PRIME FACTORS OVER ARITHMETIC PROGRESSIONS
• Linear relations of zeroes of the zeta-function
• The Second-Order Term in the Asymptotic Expansion of B(x)
• Über Zahlen der Form a²+b² in einer arithmetischen Progression