Valentin Blomer

Department of Mathematics Offices Bahen Centre, 40 St. George St. BA 6204, phone (416) 978-4436 (St.George campus) University of Toronto office hours: by appointment Toronto, Ontario, Canada M5S 2E4 CCIT 3008, phone (905) 569-4514 (Erindale campus) email: vblomer@math.toronto.edu office hours: by appointment

Teaching Mathematics

I am not teaching in the fall.
Spring preview: Theory of Character Sums, a useful and entertaining mix of number theory, algebra and analysis with applications to elliptic curves, L-functions, ...

Past graduate courses:

• Spectral methods of automorphic forms (Problem sets: Set 1, Set 2, Set 3, Set 4, Set 5)
• Algebra (Problem sets: Set 1, Set 2, Set 3, Set 4, Set 5, Set 6, Set 7, Set 8, Set 9, Set 10, Set 11, Set 12, Set 13, Set 14, Set 15, Set 16, Set 17, Set 18, Set 19)
• Introduction to Modular Forms
• Introduction to Analytic Number Theory (in Göttingen)
• Elliptic Curves and Cryptography (in Göttingen)

Mathematics Research

My area of research is analytic number theory, in particular

- automorphic forms and L-functions, and
- quadratic forms and their arithmetic applications.

Here's a list of my recent journal articles

• Thin bases of order h, Journal of Number Theory 98 (2003), 34-46 (abstract)
• On cusp forms associated with binary theta series, Archiv der Mathematik 82 (2004), 140-146 (abstract)
• Binary quadratic forms with large discriminants and sums of two squareful integers, Crelle's Journal 569 (2004), 213-234 (abstract)
• Uniform bounds for Fourier coefficients of theta series with arithmetic applications, Acta Arithmetica 114, (2004), 1-21 (abstract)
• Shifted convolution sums and subconvexity bounds for automorphic L-functions, IMRN 2004, no. 73, 3905-3926 (abstract)
• Nonvanishing of class group L-functions at the central point, Annales de l'Institut Fourier 54 (2004), 831-847 (abstract)
• Binary quadratic forms with large discriminants and sums of two squareful integers II, J. London Math. Soc. 71 (2005), 69-84 (abstract)
• A three squares theorem with almost primes (with J. Brüdern), Bulletin of the London Mathematical Society 37 (2005), 507-513 (abstract)
• Rankin-Selberg L-functions on the critical line, manuscripta mathematica 117 (2005), 111-133 (abstract)
• Uniform bounds for the number of integers represented by systems of Abelian norm forms (with J.-C. Schlage-Puchta), Acta Arith. 123 (2006), 183-199 (abstract)
• Estimates for representation numbers of quadratic forms (with A. Granville), Duke Math. Journal 135 (2006), 261-302 (abstract)
• A Burgess-like subconvex bound for twisted L-functions (with appendix 2 by Z.Mao) (with G. Harcos and P. Michel), Forum Math. 19 (2007), 61-106 (abstract)
• Bounds for modular L-functions in the level aspect (with G.Harcos and P.Michel), Ann. Sci. Ecole Norm. Sup. 40 (2007), 697-740 (abstract)
• Prime paucity for sums of two squares (with J. Brüdern), Bull. Lond. Math. Soc. 40 (2008), 457-462 (abstract)
• Sums of Hecke eigenvalues over values of quadratic polynomials, IMRN 2008 art. ID rnn059, 29pp. (abstract)
• Hybrid bounds for twisted L-functions (with G. Harcos), Crelle's Journal 621 (2008), 53-79 (abstract, arxiv)
• Ternary quadratic forms, and sums of three squares with restricted variables, in: The anatomy of integers, CRM proceedings & lecture notes 46 (2008), 1-17 (abstract)
• Spectral decomposition of shifted convolution sums (with G. Harcos), Duke Math. J. 144 (2008), 321-339 (abstract, arxiv)
• The average value of divisor sums in arithmetic progressions, Quart. J. Math. 59 (2008), 275-286 (abstract)
• On the central value of symmetric square L-functions, Math. Z. 260 (2008), 755-777 (abstract)
• A quadric with arithmetic paucity (with J. Brüdern), 10pp., to appear in Quart. J. Math.

and preprints (submitted)

• Lagrange's four squares theorem with smooth variables (with J. Brüdern and R. Dietmann), 40pp. (abstract)
• Bounding sup-norms of cusp forms of large level (with R. Holowinsky), 20pp. (abstract, arxiv)
• The number of integer points on Vinogradov's quadric (with J. Brüdern), 10pp.

I provide copies of these papers on request (see also here). The arxiv versions may differ from the published versions.

Awards

• 2003 Research and Thesis Award (University of Stuttgart)
• 2005-09 NSERC Discovery Grant
• 2005 Heinz Maier-Leibnitz Award of the German Reserach Council
• 2006 Connaught New Staff Award
• 2008 Sloan Research Fellowship

Some pictures

Johanna (Spring 2008)

Oberwolfach, 2003

Banff, 2004

Oberwolfach, 2008

A Night in Tunesia

Last Update: Sept 10/2008