On Sums of Three Squares

By Stephen Choi, Angel V. Kumchev, Robert Osburn. The Fibonacci quarterly, 2005

52 citations recorded by the source corpus.

Let r3(n) be the number of representations of a positive integer n as a sum of three squares of integers. We give two alternative proofs of a conjecture of Wagon concerning the asymptotic value of the mean square of r3(n).

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/b090060065c026536fbc4adff975f55c7bedf8a7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. V. Blomer
2. Akshay Venkatesh
3. P. Michel
4. Gergely Harcos
5. R. Munshi
6. M. Young
7. Peter Sarnak
8. Djordje Milićević

In Discrete Mathematics and Combinatorics

1. V. Blomer
2. P. Michel
3. Akshay Venkatesh
4. Gergely Harcos
5. R. Munshi
6. Peter Sarnak
7. A. Ubis
8. Farrell Brumley

Citations in the corpus

• Equidistribution, L-functions and ergodic theory: on some problems of Yu. Linnik (2006, background): “Such conceptual simplifications are particularly of value in passing from Q to a general number field; so far, with the exception of the result of Cogdell–Piatetski-Shapiro–Sarnak, all the results in Theorem 6 in the case F = Q are proven via the period approach.”
• Twisted L-Functions Over Number Fields and Hilbert’s Eleventh Problem (2009, methodology): “... place and n> 4, again Siegel’s mass formula [Si1] and bounds for Fourier coecients of Hilbert modular forms give a complete answer (some care has to be taken in the case n = 4). The only remaining case of Q positive denite and n = 3 was solved by Duke and Schulze-Pillot [DSP] for K = Q. For arbi”
• Equidistribution of CM-points on quaternion Shimura varieties (2005, unknown): “The action of the Galois group Gal(Q̄/F̃) on the connected components is given by a reciprocity homomorphism: Gal ( Q̄/F̃ ) −→ F×+\F̂/ν(U).”