Congruent numbers and congruences between half-integral weight modular forms

DOI10.1016/j.jnt.2012.09.018zbMath1282.11062OpenAlexW1967791136MaRDI QIDQ1938553

Matija Kazalicki

Publication date: 21 February 2013

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2012.09.018

zbMATH Keywords

class numberscongruent numbersBirch and Swinnerton-Dyer conjecturecongruences between modular forms

Mathematics Subject Classification ID

Quadratic extensions (11R11) Elliptic curves over global fields (11G05) Forms of half-integer weight; nonholomorphic modular forms (11F37) Congruences for modular and (p)-adic modular forms (11F33) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Class numbers, class groups, discriminants (11R29)

Cites Work

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• A classical Diophantine problem and modular forms of weight \(3/2\)
• Sur les coefficients de Fourier des formes modulaires de poids demi-entier
• Sums involving the values at negative integers of \(L\)-functions of quadratic characters
• 2-adic and 3-adic part of class numbers and properties of central values of L-functions
• 2-Selmer groups of quadratic twists of elliptic curves
• ON CERTAIN VALUES OF p-ADIC L-FUNCTIONS
• On the class number Q(√-p) modulo 16, for p ≡ 1 (mod 8) a prime
• On congruent primes and class numbers of imaginary quadratic fields
• Note on primes of type x2 + 32y2, class number, and residuacity.

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